A Stirling engine won't be a good replacement for a radiator. There are several reasons why. First it will act as a layer of thermal resistance to the cooling system of your other engine which can lead to over heating. Secondly your thermostat isn't open all the time and tends to release hot coolant in pulses (Stirling engines are only efficient with a constant supply of heat). The problem with the extra cooling area has already been mentioned.
Stirling engines work best with constant heat supply and a constant load at a constant speed. The best place for a Stirling engine to recover heat energy from would be the exhaust.
This company makes a Stirling engine however I doubt you can afford it.
Infinia Corporation
I applied there for a job last year.