Hudson,
As you realise, there is probably not much heat remaining but the reason for selecting carb heat in the drills may not be for reasons of heating as you assume.
On many aircraft, selecting carb heat allows an alternative intake path which allows air to bypass the intake filter and then go around the exhaust jacket for heating. If the reason for engine stoppage was because the filter was blocked by ice, then bypassing it may result in a successful start.
I recall some years ago, an RAF Bulldog had a birdstrike where the bird hit the intake filter and damaged it. The engine either ran very rough or failed. Selecting induction air to hot (no carb on a Bulldog, it's got fuel injection) allowed the engine to pick up and recover.
This does mean that if carb / intake heat is selected on whilst on the ground, unfiltered (gritty!) air may be ingested into the engine which won't do any good.
Hope this helps.
ShyT