Question: Is it safe to store bicycle tires near electric heaters? I'm wondering if the heat will degrade the rubber somehow. 

More specifically, I'd like to store my bike near the electric baseboard heaters in our apartment.

Answer: 
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.
Electric baseboard heaters are entirely resistive heat, so there should be no problem assuming the temperature isn't extreme.

What becomes a problem is if you store the wheels near a DC electric motor that uses brushes. These produce a small amount of ozone, which contributes to the premature destruction of tire rubber. Most AC motors are brushless, so are fine.

However, you should know that some air purifiers work by producing ozone. In addition, some office equipment such as older photocopiers also have DC motors that produce a lot of ozone. These have mostly been phased out because of health concerns but are responsible for the characteristic smell of copy machines.