(Feel free to edit your comment to add detail instead of replying; keeps the thread shorter that way.)
A tidally-locked body would have nearly 50% of its area "cold," in other words it is not radiating any heat from the primary heat source out into space. Only heat reaching the cold side from atmospheric convection or internal conduction would be able to reach space. In Mercury's case, the lack of significant atmosphere reduces the flow of heat from the warm side to the cold side.
A spheroid with any given amount of surface area exposed to equal heat / cold has the highest chance of preserving equilibrium. If that logic is true, correcting Earth's axis tilt should slightly increase the amount of energy radiated away. That would also produce more consistent temperatures between the equators and poles (raising sea levels by reducing the amount of frozen water proportionally). Needless to say that would have nearly incalculable side effects.
A hotter object loses heat faster than a cooler object.
It's actually a fourth power relationship to temperature. See Stefan-Boltzmann Law for the details.
However, the loss of ice does accelerate the warming because less light is reflected from the earth.