I’ll try here in few simple sentences explain the very essence of how the planet surface SPECIFIC HEAT "cp"warming Phenomenon occurs.
Lets consider two identical planets "H" and "L" at the same distance from the sun. Let’s assume the planet "H" has a Higher average surface specific heat, and the planet "L" has a Lower average surface specific heat.
Both planets "H" and "L" get the same intensity solar flux on their sunlit hemispheres. Consequently both planets receive the same exactly amount of SOLAR RADIATIVE ENERGY.
Depending on the specific heat capacity of bodies containing the heat energy, the temperatures can be quite different.
For Lower average surface specific heat planet "L" the sunlit hemisphere surface gets warmed at higher temperatures than for Higher average surface specific heat planet "H" the sunlit hemisphere.
The surfaces emit at σT⁴ intensity – it is the Stefan-Boltzmann emission law.
Thus the planet "L" emits more intensively from the sunlit hemisphere than the planet "H".
So there is MORE ENERGY LEFT for the planet "H" to accumulate then. That is what makes for Higher surface specific heat planet "H" to be a WARMER PLANET.
That is how the Planet Surface SPECIFIC HEAT "cp" Warming PHENOMENON occurs.