You might also want to verify that both your fans are working. The engine fan should have little resistance to spinning if it's cold. When you try to spin it it should take noticeably more effort if the car is warmed up. Some test it with the car running...a hot fan should be able to shred newspaper, but ours have plastic fins and I'm reluctant to try that.
You can test the aux fan easily by pulling the plug off the fanstat. Be careful because it tends to dissolve over the years. There are three pins inside that plug. Green is ground, black/red is high speed and black is low speed (if I recall correctly).
Get a short bit of jumper wire, turn the ignition on, and plug one side of the jumper wire into the green wire (ground) socket. Then touch the other side of that jumper wire to one of the black wire sockets. Fan should immediately turn on. Pull the wire out of the black socket and put it in the other black wire socket. Fan should immediately turn on at a different speed.
If either setting fails, check fuses and relays as described in the ETM. If the low speed fails, check (& likely replace) the resistor pack on the fan's frame. If the A/C button won't run the fan at low speed but the resistor is OK, disconnect the battery & check the inline diode inside the fuse box.