Resistance of a heating element
simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. Does adding more resistors increase or decrease the total heat produced?


  I would have thought that a higher resistance would have resulted in more heat loss ...



It should be intuitive that the more parallel resistors we apply to the circuit of Figure 1 the lower the resistance becomes.
Given a constant voltage as specified in your question it should also be intuitive that the current through each branch will be the same no matter how many branches.*
We can then see that with n parallel resistors the total power dissipated will be n times the power dissipated with one resistor.


Therefore a lower the resistance value will result in more power dissipation or heat loss.

Mathematically this can be seen from the power equation \$ P = \frac {V^2}{R} \$ that, for a given voltage, power dissipated is inversely proportional to the resistance.



* A real power supply will, of course, have a limit to how much current it can produce before the voltage starts to droop.