Is there any concern with warming up a fermentation by placing the bucket/carboy on an electric heating pad? Will it kill the yeast that settles on the bottom?
It depends upon how hot the heat pad gets - you want to use a pad that doesn't go above 30°C/85°F. I use a waterproof pad that was originally intended as a pet warmer. It has an adjustable thermostat to set the highest temperature it will reach. I have mine set to 25°C/75°F. So, even though it is connected to a temperature controller, the heat pad thermostat ensures that the underside of the carboy doesn't go above a safe temperature.
You'll want to ensure consistent temperatures. If your heating pad goes above seventy degrees Fahrenheit, you'll need a temperature controller to prevent it from going above. The ideal way to do this would be to have a heating pad that turns on the moment it is supplied power. I know a few you have to plug them in, turn them on, and then they'll run. You'll need a way to automatically have it start heating once it receives power.
Get a temperature controller. I use a Johnson Controls Digital Thermostat Control Unit. You'll need to affix the temperature probe to the side of your carboy/bucket. The ideal way to do this is to tape it to the side of the vessel, and place several layers worth of bubble wrap over it to act as insulation. If possible, try to avoid wrapping the pad over the bubble wrap, as that could heat the insulation and skew your reading. This way, the probe is getting only the temperature of the wort, and it'll turn on and off as the temperature hits the set thresholds.
Alternatively, I've heard good things about Fermwrap, but have never used one.