FF
You say its an IO-320? If its an 'I' (injected) it won't be carb icing and you won't have carb heat to select (injected engines have 'alternate air'.
Only the latest 172s are injected (P's and earlier aren't) and they use an IO-360 engine.
As others have said some engines do seem prone to icing straight after start up and idle speed over damp grass will accentuate it. The Lycoming/Cessna carb heat system isn't great as all it does is drag air over the #4 cylinder exhaust down pipe. Immediately after start this won't be very warm air. If during power checks as you say, it sounds like you have picked up ice, the initial selection clears it and then you are back to normal.
If the mixture is a bit to lean for the engine's wants then selected hot air will increase the rpm as it enrichens the mixture. I had a 152 with an induction leak once - loose stub pipe in the sump, at 1700rpm the revs increased when hot air was selected, at low rpm the 'idle' was not smooth.
If you haven't got an engineer nearby and want to check the carb heat operation, you can normally see the airbox with the cowlings on through the exhaust stub hole (although with the modded exhaust you may not be able to see this). Get someone to operate the carb heat (ENGINE OFF!) whilst you watch the arm on the side and check it moves backwards and forwards with a clunk at each end as the selector flap moves. Also ensure the outer cable is held tight and not moving in the securing P-clamp. T
This is only a visual check and if there is any thoughts of a problem then get a qualified engineer to check the system.