Car revs when shifting with defroster on

I have a 1998 Dodge Neon with a 4-cylinder, 5-speed manual transmission. When the defroster is on the engine races when I depress the clutch to change gears. What is causing this?

I am going to take a SWAG. The defroster activates the air conditioner. (it helps dehumidify the air) and the extra power drain from the AC running causes the idle speed to go up.

Does the engine race when the A/C is ‘on’ and cooling? I assume this car has Air Conditioning. Does the A/C work?

Your answers will help us diagnose.