If there was a way to turn off the fan I could simply put tape over the vents and it would probably work a lot better.
What about the following:
If the only measure you take is to block the vents then it is likely that the problem will recur because despite the measure, the back will be at ambient temperature. Ideally you want the back electronics as warm as possible, since reliability is known to exist at elevated temperatures.
It may be awkward, but if you were to carry the back on your person as you do your batteries, then the back will be warm. Of course it will rapidly cool when exposed to the environment. However, if the vents are covered then the fan will circulate only the internal air volume, which will be relatively warm at the time the back is switched on.
With the vents blocked the back normally will begin to heat up. However, given the low ambient temperature, a temperature gradient will exist through the back and will help to dissipate heat from it. It may be that the temperature gradient is large enough for the net effect to be a gradual reduction in temperature of the back internal volume, or it may be that the temperature gradient is not large enough and the back gradually heats up to the point whereby (hopefully!) it shuts down to prevent internal damage from overheating, albeit the latter intuitively strikes me as being unlikely.
The point is that even if the back still fails from reaching too low or high a temperature, the act of taping the vents may help to extend
the time the back is operable.