To me, the answer is obvious by observation. I can't do the math, but if someone would care to dope it out, here is my theory.
If we eliminate designs that are specific to heat conservation, such as double walls and lids, and make it strictly a single-walled material with an open top: a mug which angles inward to a narrow neck and top from a wider bases keep coffee warmer longer--a mug with a conical base incorporated into it.
This shape takes advantage of the common property of heat and steam-- they RISE. In a standard cylinder, most of the steam and heat escape upwards into the air. But the conical body allows for more steam and heat to make contact with the upper body of the mug and heat the material, which in turn warms the coffee.
As a standard cylinder mug's coffee is consumed, the same upward trajectory for heat remains constant because of the uniform circumference. More inner wall is exposed, but the wall is also making more contact with cool air and is ineffective at retaining and transferring heat back to the coffee, either thru transference to the deeper liquid layer or the surface layer.
But in a conical mug made of the same material, the steam/heat from the outer edge of the coffee is channeled along the acute angle of the inner wall. More heat and steam is retained longer, utilized within a more contained chamber before eventually reaching the narrow neck and opening. Some steam might also begin to condense into drops which return to the coffee.
Other advantages: Less likely to tip because whether full or empty, it is always bottom heavy.
Disadvantages: Harder to get clean, and most likely won't be cleaned at all in a dishwasher.