What is causing my light bulbs to burn out so quickly?
Both the voltage and temperature could be culprits here - many bulbs are sensitive to overvoltage.

If you are going with LED bulbs, you usually have a wider acceptable voltage range, but you should be able to get the max-voltage info before you buy.

Additionally, LED's have very low heat output, so will be just fine in the enclosures.

So I'd say the problem will be solved by getting LED bulbs (just check that max-voltage on the spec first) - these will last so much longer.

Alternatively, If you are handy with electrics, have a look at the power supply circuit and see if you can reduce the voltage. Are all the bulbs in series? If so, adding a power resistor will drop the voltage (at the expense of some heat generated across the resistor). If the bulbs are in parallel, you'd need to see if there is a voltage control on the power supply itself.