It is a great idea to plug the thermostat into the surge protector! I refuse to have my reptiles or computer plugged into the wall socket. We have surges/brownouts or blackouts happen in my home. I do not want an errant current to fry my thermostat and risk injuring my scaley kids.
The surge protector would not affect the thermostat since it is reading the temperature of the heat source you have plugged into it and is affecting the powerflow only to that product.
If you are plugging a surge protector into the thermostat and plugging heat sources into the strip.... that is a different story. different heat strip sizes use different wattage or heat differently, so that strip should only house one size of heat strip. Do not mix up heat types. And it's recommended to temp check every heat source as well to verify they are functioning properly.