1995 Ford Explorer XL, factory stereo stops working only on hot days.

It does sound like a heat related electrical problem. Since the radio is electronic, at first thought, I would believe it is there. But since both radios act the same the problem is probably elsewhere. Does the radio simply stop working or does it turn off? You can try this. When the radio is not working check all the electrical connections on the back with a multi-meter. If power is not being supplied begin back checking/probing the connections with the meter.

OJ > The radio completely stops working - won't respond to the power button...until the temp either under the dash or the hood cools down below 85°F (roughly). I have found that the battery terminals under the hood are terribly corroded. I'm surprised the motor even cranks. I'm off today so I'll be cleaning those connections. Though with my luck it won't be that simple. I do have a multi-meter but still learning how to use it. What setting should I use to check the connections behind the radio. Also for the fuses and harness connections too I'm assuming?

Not knowing what type of meter you have this explanation will be generic. If your meter has a setting labeled "V" or "voltage" set it to that. You will have to determine if the meter has another setting for DC voltage. Set the meter to DC voltage. The reading you get should be 12 or close to that figure. You will have to determine which wire plug out attached to the radio is the positive and which is the ground. The positive is often black or black with a white/colored stripe with the ground being white, but this is not always the case. If you still have the paperwork which came with the radio, check the schematic. The pin-out diagram should show which wire is which. Simply lineup the plug on the radio with the corresponding power supply under the dash to determine which color wires are positive and negative.

The fuse can be checked with the meter set to "continuity". Once that setting is chosen, simply touching the black lead to the red lead on the meter will either cause the needle on the meter to swing on an analog meter. ON digital meters you may hear an beep or tone. Continuity just means the circuit is closed and current is flowing through the fuse. I doubt the fuse is the problem.

Keep in mind the non functioning condition must be present when testing occurs or you will never find the problem. If you determine voltage is not being supplied at times you will need an attachment for your meter to make things easier. It is nothing more than a sharp pin point attached to the positive lead on the meter. This allows you to probe the positive wire withing stripping off the insulation. Simply pierce the jacket on the wire with the pin then use the ground wire on the meter, touching it to any non-painted metal surface on the vehicle to complete the circuit. When current is present the meter will read 12 volts or so.