After 3 weeks of running at 110 VAC and after hooking it up to 220 VAC I am convinced that the case temperature is about the same for both voltages.
I have no doubt that the fan could have run for years at 110 VAC.
However, at 220 VAC the CFM output is much greater than 2X. I would guess 3x or 4x.
Running this 1/4 hp 220 VAC fan at 110 VAC was ~2 Amps or 220 Watts.
At 220 VAC it also pulls ~2 Amps and therefore 440 Watts.
If the CFM is OK at 110 VAC and QUIET is your goal, 110 seems OK..
For the best CFM output/watt use 220VAC.
My attic is now in the 80's and we can all feel the difference.
If the cost savings turns out to be zero, it would pay to run the fan for the comfort received.