The APU is a constant-speed turbine engine, which means that it's RPM is constant. This is achieved by the fuel control unit, which schedules the amount of fuel required to keep the engine turning at constant speed, therefore the only true way to see the engine load is through EGT: if you increase the load on the APU, more fuel will be required to turn it at constant speed - more fuel, the higher the EGT as in any turbine engine. One positive thing of APU being constant-speed engine is that you don't need a CSU between the engine and the electric generator, as the APU itself is turning at a constant speed.
I stand to be corrected though.