You don't have to understand the internals of solar panels, although that is helpful because it's nice when things agree.
Basic understanding of conservation of energy is enough. Clearly shorting/opening solar panels do not affect the emissivity of the panels much (this would be visible to eye), so the heating of the panel has to be similar in both cases (open and shorted), where no external work is done. Only when significant output power is generated into external load, only then the panel can run cooler, because energy is extracted from the system.
Now if you understand how the panel works, and the equivalent circuit of the diode turning on, clamping the cell voltage to certain open-circuit voltage and internally dissipating generated power, you can see these two mental approaches agree, which is nice.
The only thing which does not agree with this is nctnico's intuition, but this is no news, we can see every day this is something not to be trusted.
For the OP, the best solution, by far, is to install an inverter and start putting the investment into use. Second best solution is to try to use the generated power to heat water with a resistive heater or do something mildly useful like that.