It supposedly causes wear due to running too cold for too long, fuel wash in the cylinders from the choke, once up to temperature it will make no difference. Some say without one the coolant moves too fast and doesn't have time to absorb or dissipate the heat, but a well made thermostat has a pretty big flow rate, so not sure that holds true. Their purpose is to let the engine heat up quicker because a hot engine is way more efficient than a cold one.
If the radiator isn't up to the task, then it doesn't matter what thermostat you have, it will always over heat if it can't get rid of the heat. Thermostats have little effect on dirty blocks as long as they open.