Five months later...
I wanted to share my experience with another firebrats culture with you. Meanwhile they have become one of my favorite feeding-insects culture: very easy to maintain, not much to care about and after a rather long initial time (first reproduction cycle from egg to egg-laying adult about 5 to 6 months!) they are rather productive.
My setup:
Since I do not have a warm room with more than the necessary 30 °C, I used a styrofoam container as mentioned earlier:
Inside of this container I attached a 20 Watt heating cable, normally used for aquaria or terraria. To make sure that the firebrats do not get roasted, i fixed the cable on the sidewalls of the box and not on the bottom.
For temperature control I used a small thermostat. In the picture you can see the control unit outside the box and the sensor inside of it:
For a container itself I used small plastic containers with a volume of 10 liters (3 of them fit into the styrofoam box this size). Inside of this container I placed several egg-packings (might be the wrong word for it) and inside these things I placed cotton wool pads. The firebrats use these as a substrate for their own eggs, after several months they turn orange-grey, the orange part is supposed to be the eggs.
Firebrats must not have direct contact to water, but they need a small amount of humidity and so I used a small glass, filled it with water, covered it with part of a pantyhose and placed it inside the container:
Finally I added the firebrats and some food. I use fishflakes and oat flakes as a food source but they will also nibble the paper / cardboard of the egg-packings, so they can be left on their own for several weeks if necessary.
First I covered the container with only another piece of pantyhose but I found out that the humidity obviously was too low and several firebrats died (thanks for the hint to Ralf!).
So meanwhile I additionally use a plastic plate on top of that and the culture is going very well and I have a steady supply of firebrats.