Wow, this is kinda outdated, so... update time!
Well, I tried a 15W heating cable but it didn't really work out. There was just a tiny bit of condensation at the top of the tube but after a while the workers started to extensively groom the larvae and what I think they did was they actually tried to cool them as the tube got too hot. Since the room is already at ~25°C and the ideal nest temperature for them is 24-28°C I won't heat them anymore. They should be fine with room temperature.
Also working with them got a bit tricky since they become some sort of Ferrari racing ants when the temperatures go higher.
Next thing is, these little creatures are smart. They've already learned that when their tube is shaking usually something "invades" their nest (= the food I push through the straw with a wooden stick). So as soon as I touch the tube one or two of the workers will run to the front chamber and stand guard which means I have to wait a few minutes until they calm down again before I can add any food to their tube (the queen doesn't care btw, it seems she always stays relaxed, even when two workers are running around like mad waving alarm flags).
I also had to clean out the front chamber of their tube (remove the cotton, brush everything out, wait until they calmed down, put cotton back in) since they wanted to dispose the crickets but weren't able to do so because the dried hardened legs didn't fit though the straw. As a result they now get legless crickets (I remove the legs before feeding them).
Adding a sugar water tube was a good idea, these ants drink sugars in bursts. The sugar water level doesn't change for days, then over night suddenly a huge portion goes missing.
Their appetite on protein is fine so far. After some fruit flies and crickets I caught a big spider in my kitchen which was feasting on the wild fruit flies there (it had almost the size of the queen). After a day in the freezer I removed the legs and put it into the tube. It got the regular greeting ("I don't know you, have some formic acid") and two of the workers seemed fairly interested. When I checked on them the next day the spider was gone. Like, literally gone. I can' find a trace of it anywhere, it completely disappeared. No idea what they did with it but the queen looking like a replete (her gaster is essentially transparent) is a good hint - I guess she just ate it entirely the way she likes to do with the fruit flies. Maybe the larvae ate some of the harder parts as well.
Speaking of the larvae, they have picked up in development. The largest one is now really big, larger than the nanitics (still no sign of it pupating though) and the smaller ones also have doubled in size. Plus a few days ago the queen laid a new batch of eggs.
Finally, yesterday I fed them some raspberries (actually it was two of the tiny bubbles that make up a raspberry and yes, they also got the acid greeting). It was really interesting to watch them eat these - they ripped off tiny bits by biting into it and then quickly pulling back, I've never seen them doing something like this before (wait, now that I'm mentioning it I did see this before when they encountered dead insect food - but I always thought that was more of a "is it dead?" test). They were pretty well-fed already so they didn't eat much but they pushed them to a dry cotton part which usually means they like it and wanna keep it so they can eat it later.
Since they are so extremely well-fed I decided to not disturb them at all for a week and just let them do their thing. Maybe I can report the first pupa then, or a new batch of larvae!