Look into something like flexwatt tape. Maybe run it during the day when your not sleeping. In my mind, they probably use something similar inside heated blankets with some kind of limiter/thermostat.
Do your research though!! I'm not sure if flexwatt tape could ignite your mattress, but you would definitely want to know for sure yourself beforehand!
There are ways to control heat though; I'm familiar with using flexwatt tape with reptile enclosures, hooked up to a thermostat with a probe in the habitat for temp control. Maybe some math, like desired_temp = watts_supplied * feet_of_fw_tape, where the watts_supplied is the independent variable you adjust based on the required feet_of_fw_tape for your mattress to get the dependent variable desired_temp. Probably include a fail safe, but I'm no electrician, proceed at your own risk.
They do sell self contained fire extinguishers you can hang on your ceiling that deploy automatically at a certain temperature, ideally putting out fire sources they are hung above. Nice to have around for things like this.