To clarify, I am doing this to determine the efficiency of the motor for design verification purposes. It only needs to happen once.
The FETs are fixed to the board. I can not measure the current through the FETs because they are fixed to the board, only the voltage across them. There are sense resistors which will allow me to determine the current through the low side FETs, which will allow me to integrate current by voltage over time. But because it is a 3-phase BLDC motor, if I know the current flowing through a bottom FET, I still don't know the current flowing through the top FET. So I am still unable to determine this. Because a charge pump is used to generate the gate voltage for the high side FETs, I am concerned that the gate voltage may not be symmetrical to the low side gate voltage.
The thermal approach is tempting, and I will do it to verify my voltage/current based approach. I can do it for the low side FETs at least.
I was hoping for some clean mathematical solution, but I don't seem to be able to find one. Using V^2/Rds(on) is still an approximation, because I don't know my gate current, either.