Ok.. Here's what I did. Nothing scientific but proved a point..
The power supply has a potential of 50 amps and voltage adjustable between 0-15 volts..
Across a 4 ohm wire wound resistor, I applied 3 volts with unbridled current. The resistor warmed up but didn't pull very much current. I then increased the voltage to 12 volts (4 times) and it showed more current draw and heated up much quicker! The same resistor made more heat and drew more current by increasing the voltage..
Never claimed to be an engineer but I can see that my vision on what should happen was wrong. I'm a good sport, though. I'll take my beatin'..
Anyhow, after thinking about this a little more, maybe your choice of a heat producing device could be replaced with something with less bulk than those big resistors. It would take some energy just to heat those big boys up!
Perhaps a toaster or part of a heating element from a drier?