If Earth did not retain the heat from its formation, the most likely event that would occur is that the asthenosphere and outer core would solidify.
The retention of heat from the planet's formation, along with radioactive decay, contributes to keeping the outer core liquid and the asthenosphere (a semi-fluid layer of the upper mantle) partially molten. If Earth lost this heat, these layers would cool down and solidify, which would significantly impact geological activity and the dynamics of plate tectonics.