Pretty much any automotive relay would work for this.
Be aware of the kind of thermostat you're using. Many household thermostats use a mercury or similar tilt switch that is mounted to a bimetallic strip (like in a dial thermometer). If such a thermostat is not level, the temperature setting will be inaccurate; also, jostling may cause it to bounce on and off. (Many of them are calibrated/adjusted by tilting the internal mechanism, in fact.) Neither of these is much of a problem for a normal house, but in an RV conditions are different.
As for why do this rather than just buying a Fantastic Fan: one reason is that there is a very real difference in cash outlay between fiddling with a thermostat and a fan that you already have and purchasing a Fantastic Fan....