I am a keeper of two species of ants from the genus Cataglyphis, rosenhaueri and nodus, both for about a year now. This genus is known for their preference to forage during the hottest hours of the day, rushing at astounding speeds to do their job before they collapse due to overheating. It's an adaptation to fill a niche - they avoid competition and predators by foraging when it's too hot for them. They can also collect freshly heat stroken insects. Their heat tolerance, while higher than of competitors, is with limits, so their thermal window of opportunity is small. The most known species of this genus, Cataglyphis bombycina, is known to sometimes be able to forage for just 10 minutes - that's how short it takes for the temperature to rise from "too hot for predators and competition" to "too hot even for them".
There are more genera of ants known for same strategy, Aussie keepers are familiar with Melophorus, and Ocymyrmex from South Africa are known to be adapted for just as extreme environment.
For keeping such ants I think it's beneficial or even necessary to provide heating and lighting of the outworld during the day to stimulate their instinct to forage during scorching midday.
The most primitive method would be placing the outworld in a sunny spot. This is a poor soluton since the intensity of sunlight will vary day to day and over the year. Even assuming this is most natural, since that's what they experience in nature - I don't think their outworld will get as hot as soil surface gets outside with a glass window in the way and air temperature inside being usually colder than outside during the day.
Another method is a LED light and a heat mat. This sounds great at first as it allows for arbitrary and independent temperature and light intensity setting. I personally decided to never try it, as in my opinion it would be comparable to walking on hot rocks in the evening rather than scorching midday sun, since all of the heat would be coming from the bottom, and light would not bring any heat.
I opted for using a halogen lamp. It provides both heat and light at the same time, and I think the heat comes to the ants in most natural manner, as it's coming in form of infrared radiation - it heats the ant body from the top just like Sun would. It's not exactly like sun, but I think this is the best compromise.¹ It also just looks really neat and natural, leading to pleasant observation and photography of the ants.
I have observed that both colonies like the heated part of the outworld very much. Cataglyphis rosenhaueri are mostly running in the heated part of their outworld. I often see Cataglyphis nodus climbing the rock in the picture even when there is no food to be found there. It's closer to the light bulb, resulting in temperature over 50°C on top of it! I think they come there due to their heat loving instinct telling them it's a better spot for foraging. I am thinking about changing the bulb for a 35 W one to see how will they react to even higher surface temperatures.
For reference: I use 20 W 12 V bulbs in MR16 size format (bulb with a reflector part forming a beam) placed around 23 cm away from soil surface, which results in about 20 K temperature increase directly under the bulb. Of course this will vary between setups due to differences in soil reflectivity, air movement, etc., so take this value with a grain of salt. I provide this data just so you have any idea of order of magnitude of lamp power needed to achieve a soil temperature increase.
I run the halogen lights for about 10 hours a day. I do not have much experience with hotness of deserts, but I think that's enough time to simulate the hot part of the day. Cataglyphis rosenhaueri commonly stop foraging a good while before the light turns off, suggesting they understand that day will come to an end at some point and after x hours pass it's safer to cease activity before competition/predators become active again. C. nodus are less bound by their diurnality, but their behaviour also supports the concept of heating the outworld during the day.
Some things to take into consideration:
- Reflector material of your bulb. TL;DR there are two types available: a dichroic coat or aluminum coat. Dichroic coat is designed to pass the infrared part of radiation through it, to the back of the bulb. It's good for using the halogens as exhibit light, but it's terrible for using it as a directional heat beam. You need the aluminum coated reflector. I found out that if the bulb is not sold as intended for terraristic purposes, then it is practically guaranteed to be dichroic, so unfortunately - it makes sense to buy the expensive terraristic product rather than 3-4x cheaper general purpose halogen bulb... I use LUCKY REPTILE Halogen Sun LV and they are working well for me, creating a 20 cm ring of light - leaving plenty space on the sides of the outworld for thermal refuges.
- For bulb housing I just bought some cheap home ceiling fixture,, replaced the socket inside, made a hole for the cable, secured the hole edge so it won't cut into the cable and called it a day. It costed about 4€ and even has a mechanism for rocking the bulb to change the direction of the light beam a little. You must make sure the fixture is rated for the power of the bulb you're going to use! And now, in the era of LEDs rated at "incandescent equivalent power" you have to be extra careful whether the rating is not for this equivalent LED only...
- While halogen is very efficient at radiating heat from input energy compared to incandescent bulbs or ceramic infrared heaters, it still is wasting a lot of energy. This means two things: increased electricity bill and heating of the shelf ceiling. You should be very careful about placing any animal setup directly above the desert setup as you can very easily overheat it.
- You might want to use a low voltage bulb variant. Due to some black magic (which I can explain if you're really curious) low voltage halogen is more efficient (you get higher surface temperature from same electrical power consumed). This unfortunately means you need a power supply too. Fortunately there are cheap circuits specifically for halogen lamps available - they generate quite a lot of electrical noise, though. Another, more practical problem is that they have a minimum power rating - you can't plug a 10 W bulb to a 20-60 W power supply, it will fail to operate reliably.
If you don't feel like understanding any of it, just screw the (advertised 25%) better efficiency and use mains powered halogen bulbs for peace of mind and simplicity. Keep in mind that due to me using the LV variant, you will get lower temperature from a 20 W in same setup as mine.
¹ For nerd reference: Sun surface temperature is 5772 K, and to match sunlight we would need an incandescent bulb being able to run that hot. This is impossible, since the metal used for filament melts at about 3700 K, and nothing better really exists. Halogen bulbs use a clever chemical trick to prolong life of the filament at high temperatures, allowing them to operate it at temperatures up to 3400 K. At this temperature the spectrum is infrared shifted compared to Sun.. resulting in relatively more heat compared to visible light being generated. I personally don't think ants really mind the visible light intensity being only 1/5 of what they would experience in nature. See graphs in the link below to understand how much does temperature of the filament affect the spectrum.
A halogen lamp is a special variant of incandescent lamp, which has some halogen added to it. Due to how it interacts with tungsten it can be operated at higher temperature for same lifespan of a bulb. Temperature of the filament dictates the output spectrum of the lamp and amount of energy radiated, which is why halogen produces whiter light and more radiated heat than standard incandescent light of same electrical power consumption.
Some heat probably comes through convection, too. I bet you'd get more result if you'd hang a 2 W incandescent bulb above the outworld, especially with any form of reflector. My first reflector for a dichroic coated bulb was just a piece of metal sheet. 
