In this circuit I used a 20 amp relay that was re-used from an old hot tub controller. The standard outlet is modified by breaking the hot connection between the two outlets so that the one outlet is hot all the time for the wall-wart and the other outlet is hot when the circuit board commands.
This Digital Thermostat circuit board should be extremely accurate. One can purchase either the Centigrade or Fahrenheit model. There is a probe that comes with the board which is attached to about a foot length of wire. The board has an accuracy of 0.1 degree Centigrade and can control with just a 0.1 degree of change. It can be configure to energize the relay if it either gets too cold or too hot. The board has memory even after power is removed so that one does not need to reset after power is reapplied.
Relay on right side
Digital Thermostat board