Yes.
After the engine quits there is residual "heat" (bad term, sorry you thermodynamicists) everywhere in the engine compartment. If you are lucky, the ice will melt because the entire engine is warm.
"heat" is not a noun. There is no such thing as "heat." If you open an oven door and look in there is no "heat" in there. There IS high temperature air.
If the carb iced up, it's not going to deice itself due to warm air in the engine compartment. The temperature drop in the carb is due to two factors: the pressure drop in the venturi (good for about 30°F, IIRC) and the evaporative cooling caused by vaporizing fuel (another 40°F or so). The total is around 70°F, and can cause ice IF the humidity is high enough, and the carb setup is prone to icing, on a 100°F day.
The only heat that reaches the carb that will remove already-formed ice is the carb heat, usually from a muff on the exhaust pipe or muffler. If you ever have a chance to examine those parts when they're off, you'll see that they are very thin and light and won't hold heat very long, especially with air flowing around them on the way to the carb. They can stay hot after landing, but there's no airflow cooling them at that point and it's not a good indication of residual heat available for deicing. Once an engine quits due to carb ice, you have very little time to retrieve it. Get the throttle open all the way, since part of the trouble is air starvation. Some carbs will ice up their fuel nozzles, too, and cut off the fuel flow, but that's less likely.
Sometimes the throttle is already all the way open when it quits, since the unsuspecting pilot kept opening it a bit more as the RPM was failing. I have seen that happen on the ramp after a runup; the engine tries to die when the pilot closes the throttle, and so he just opens it some to keep it going, not realizing that it's trying to tell him that it's going to die if he doesn't wake up. A long taxi after runup can also create enough ice that there isn't enough power available to get out of ground effect.
The sad thing is that there are far too many engine failures due to ice and the lack of pilots' understanding of it and how to handle it. Accident investigation reports are full of phrases like "carburetor icing was suspected, since conditions were conducive to induction icing and no mechanical, fuel or electrical faults were found with the engine or aircraft." The ice melts due to engine compartment heat (or environmental warmth) after the accident, and the proof is gone. And many times, if the accident didn't wreck the engine, it will start and run just fine afterward.
Dan