It may not absolutely require a cooling fan, but having one sure does make the system last longer. The C64 power supply, and the external disk drive on the TRS80 are two prime examples of equipment that have no cooling fans but that desperately need them. Both are prone to failure due to overheating. At very least, place the equipment so that the heated air can vent easily. Cleanliness is also important, especially around mechanical devices.
Dust is a serious enemy.
Especially here in Arizona, you won't be able to eliminate the problem of dust entirely. Use a slightly damp cloth so that the dust gets picked up and removed. Do NOT use something like a feather duster. All this will do will be to scatter the dust further - often to the more tender areas of your system. Cleaning of disk or cassette drive heads is presently in a controversy.