yes it will martin, and yes, Ohms law does apply here as the temprature is directly proportional to the power (wattage) as that power has to be disipated somehow and somewhere.
Power = volts^2/ohm
so if the resistance does not change, but voltage increases, that means POWER increases. Has no choice.
12v^2/1000 ohms = .1444 watts
24v^2/1000 ohms = .576 watts or an increase of .4316 watts.
That power has to be disipated somewhere
Why would MoTeC want to run cooler with higher voltage? Simple, more over head as at 24v you have decreased the overhead as now it is easier to pull more amperage which means more power draw.
IE let say that you pull 100amps from the 12v system v 100A of the 24v system.
That is 1200 watts total from the 12v system v 2400 watts of the 24v system for a net increase in 1200 watts, which if you were to run the PDM at the SAME temps, the 24v would reach it's temp limit threshold before it even gets to 60 amps @ 24 volts. Hence run it cooler.