I'm with SSD on this, purely from a mechanic's perspective.
Heat will tend to soak back from the cylinder to the manifold , therefore, other than carburettor -ice, I'd expect any formation to be part-way along the induction-tract....but the carb. venturi would tend to freeze the moisture out first......add carb heat, -FUNDAMENTAL TEACHING, - If engine runs rougher, it's carb ice melting LEAVE HEAT ON !!!! A carb with fixed-mixture may actually run better, as the heat will lean the mixture slightly .. the effect of the warm-air blast on ice is probably only a few seconds before it starts to melt, However, As SSD suggests, It would probably take in excess of 10 minutes at lowish power-settings, to heat-soak the Carb. body to any useful degree.
For my money, carb heat in the circuit if there's the slightest chance of ice formation....bung it in on short final and you can be confident a clump of ice is not going to spoil a sudden decision to go-round....On a short strip, that sudden cough and splutter could be a really bad thing.
The loss of power with heat is not that big-a -deal, IMO, as the aircraft is not taking -off, so it's got less drag and needs less power (also may be in ground-effect) It's by far the lesser evil. momentary application of carb heat can be dangerous, as explained above...a monimum of 30 seconds should be about right. to be certain..
The only downside, other than the small power-loss, is the fact the warm air is unfiltered, but the air is relatively clean aloft, compared with ground-level and tyres and turbulence stirring up dust....carb heat still makes sense as a wise precaution.