I will be pulling this Time Capsule apart, replacing the failed capacitors in its power supply, and modifying the case so that it runs cooler. I will cut a hole in the bottom of the case and place the fan so that it draws in fresh air and forces it into the case, where it will escape from the vent slits. I will then wire the fan directly to the 5-volt output of the power supply, so the fan runs whenever the device is powered on.
Forced air cooling in this manner will bring the internal temperature down to reasonable levels and allow the device to keep functioning for years. If I only replaced the capacitors, the device would fail in the same manner in another two years or so, because the capacitor failures are only a symptom of the real problem of overheating.
I will be charging for this repair, because my time is valuable, I hadn’t really planned on this until it sorta appeared in front of me to do, and I can always use a few dollars here and there. Compared to buying a new device, my repair will be quite cheap :P