The heat is coming out one way or another. It already traveled 6500 km to the surface unaided, we're just helping it up the last 1 km or so. Frankly, I'd be interested if the core would notice an effect from the removal of the Earth's crust in it's entirety. My money is on "no for any human-relavant-timescale."
For reference, the interior of the Earth works out to about 50 TW of heat. Today, humans consume about 20 TW. The Sun delivers 173000 TW.
https://en.wikipedia.org/wiki/Earth%27s_internal_heat_budget