To add to Pete's post, mine was doing a similar thing - when driving on a medium-hot day (mid 80s, high humidity), my temperature gauge would rise alarmingly when I turned the AC on, and would slowly come down when I turned it off, but this required me to drive it very gently, and coast a lot. Soon afterward, I started my track car conversion project, so I haven't driven it in a year and a half. But as I was installing Pete's dual oil coolers, I stumbled into this:
The insulation around my fan switch wires had somehow gotten torn off, allowing the wires, I'm sure, to either touch each other, or maybe even a chassis ground point, as I was driving the car. Note: the above picture was taken midway into my repair, where I cut the wires completely and re-connected them using butt connectors - I thought I had snapped a picture of the wires before I started the repair, but apparently not. Before you spend any money on anything, you might want to take a quick look at all your fan's wires and make sure they're all intact.