I'm a layman, but my mental model suggests that tidal-lock would be the relationship that raises the energy most on the receiving body. An example of that concept would be Mercury.

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.

The other day I had a random urge to Google why sea levels are actually rising, and I learned that it's not a result of melting ice. Melting ice and rising sea levels are both the result of rising temperatures. The sea absorbs the heat and expands.

However, the loss of ice does accelerate the warming because less light is reflected from the earth.

I don't think that right. The hotter side would radiate more than if the same amount of energy were distributed over the whole planet surface.

Yes, there is a simple puzzle that makes use of this. When carrying coffee back to the office, how do you insure that the coffee will be the hottest, by putting in the cream at Starbucks or back at the office?

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.