I agree it seems to make complete sense that if the air is warmed to the dewpoint, moisture will form, and hence ice could be prevelant.
No, it doesn't make any sense at all. Where does this moisture come from?
I've come across the claim of carb heat having the potential to cause icing in cold temperatures, but I've never seen a convincing mechnism proposed for such icing except where the aircraft is in visible, glaciated moisture (e.g. cirrus).
To understand why, look at the reasons for the bounds on conditions that cause carb icing. Take a look at the susceptibility chart in the
AIC.
For saturated or almost saturated air, it is indicated that carb icing is possible from -13 degC to +30 degC and the highest risk is between -2 degC to +17 degC.
First the upper limit. How can it be too warm for carb ice? Because the temperature is suffciently high that the drop caused by the induction constrictions (of 20 to 30 degC) doesn't cool it below 0 degC.
Now the more interesting lower limit. How can it be too cold for carb ice? Because the amount of moisture that the induction air can hold varies strongly with temperature. At -2 degC the water vapour content is less than 25% of the content at 20 degC. At lower temperatures, there's simple not enough water vapour in the air to be likely cause a problem.
It makes no difference if we subsequently heat the air before it is cooled in the rest of the induction system. The only way of causing icing at lower temperatures is to add more moisture. I can see only one mechanism for adding moisture by applying carb heat, and that is by melting ice that would otherwise have been prefrozen and therefore not have iced up in an inconvenient place like the venturi or throttle butterfly. That means snow, or ice crystals such as in glaciated cloud.
If you're flying along in cold (and therefore dry) unsaturated air, carb heat will not cause induction icing.