Reddit mentions of Venstar T1100RF and T1100REC Wireless Digital Thermostat Kit

Well, there isn't anything wrong with the thermostat, the problem is that your heater is now too close to it. So what happens is, you set the thermostat for 70, the heater turns on and heats up the air near the thermostat, and then the thermostat turns off before the rest of the room gets warm.

Baseboard heaters should be located along outside walls, especially under windows, whenever possible. Thermostats should be on an interior wall and never anywhere close to the heater or any other heat source.

The way to fix it is either to relocate the heater back to its old location, or to move the thermostat. Depending on where the thermostat wiring goes would determine if this is an option, but it would require making holes in walls and I don't know if you could do that in a rental.

The other option is a wireless thermostat, something like this. They are pretty pricey, but they let you put the control unit in one location and the temperature sensor in another, and they communicate wirelessly.

I used one of these in my old house where the t-stat was too close to the woodstove. The receiver goes where your wired t-stat is and the main compenent is movable throughout the house. You could just stand it in one of your kids rooms. It was much cheaper when I bought mine 3-4 years ago, so search around:

http://www.amazon.com/Venstar-T1100RF-and-T1100REC-Thermostat/dp/B006R6BN02