The "heater" is a peltier with two heatsinks attached to it. They are a bit isolated from each other from a 4 layers of painter fleece. Seems to work pretty well. The hot side heats up to ~37° after half an hour. Very slow but slow is anything but bad in this situation. If something should ever fail. The chance of the plant to overheat is very slim and the chance of my box to go up in flames as well.
The peltier gets controlled by an Arduino Pro Mini clone, an N-Channel MOSFET and a thermistor probe that sits in the seedlings soil. I just measured what resistance the thermistor had at certain temperatures and entered these values as a threshold into the Arduino code. I don't have a datasheet for this thing so anything else would have been guess work.
I cut a few holes into a small project box with my router and put in a few connectors for all the connections needed. For the screw terminal that I used to connect the peltier to the MOSFET I just pressed the leads of the terminal against the case and drilled 1mm holes where they left their mark. That made a tight fit so I didn't even had to glue anything there.