Heat dissipation from pcb
You can measure the power in using standard methods. 

So we need to measure the power dissipated into the heatsink on the reverse of the PCB. The best way to do this is to fully insulate the heatsink thermally, so only the top of the PCB is exposed. Now, if you know the mass of the heatsink, the specific heat of the metal, measure the temperature rise (with a thermocouple?) over a certain amount of time then you can calculate how much power is being dumped into it.

If possible replace the existing heatsink plate with something more massive so the temperature rise is not so fast. Remember, the heat sink now will not be dissipating any heat at all (ideally).