Will electric heaters degrade bicycle tires?
It depends on a lot of hows including (but not limited to) close, hot, long, and manufactured.  

Most well manufactured tires that are mounted and aired up will mostly suffer from air loss.  As the tire and tube heats up, the pressure rises and the tendency to leak a bit of pressure over time will be exaggerated.  Tubeless setups utilizing juice may see that juice evaporate/dissipate quicker.  Tire/tube setups that were recently inflated to max pressures in much colder environments may actually blow out (happened one time when I left a wheel in front of a sunny window).  

If you are talking about storing your bike along side a baseboard heater or similar, you are probably going to be ok short of actually leaning the tires directly against the heat source.