you have to measure the current through the pelts while they are running. To do this you connect the pelt in series with a multimeter set to measure current. Then run the pelt and see what the current is. The power = Voltage*Current.
One problem you may run into here is that if it is a high power pelt it will be drawing around 20 amps from a 12 Volt line. This is more current than a lot of multimeters can handle, so check the specs of the multimeter so you don't fry it.
Also, the resistance and current of the pelt are dependent on the thermal load on it, and it's temperature, so you should try to measure it in as real of condition as possable, with a heat load and a heatsink. Wait for the whole system to reach steady state as well, ie. the temperature of everything is stable.
If you can't find a multimeter capable of measuring the current, you can find the power by measuring the resistance of the pelt. This won't be perticularly accurate, as you can't measure the resistance while it is running, but it should give you a close idea. To find the power, measure the resistance, and then, Power = Voltage^2/Resistance
This power value will probably be higher than the actual value, as the resistance will increase as the pelt heats up, but it should at least give you some idea.
What do you mean about the heatsink not being able to keep up and it stops working? Do you mean the temps start to go up, or that the pelt totally cuts out?