Question

How does the greater size of sun make it hotter than earth?

Answer 1

if size is proportional to mass, more mass=more energy (heat)

Answer 2

The sun's internal gravity is so strong that protons at its center are forced very close together near the center of the Sun. When they get close enough together, they undergo
nuclear fusion, which releases energy and heats up the interior, and ultimately, the entire sun.

The earth, being much less massive, doesn't have strong enough gravioty to force the protons close enough for fusion to occur, so energy is released and the earth is cold(er).