For radiation heat transfer, "heat" transfer is defined as the net energy transfer after radiation energy flows in both directions are considered. Earth's atmosphere absorbs about 358 W/m of thermal radiation emitted by the surface, and emits about 340 W/m back to the surface—yielding a radiative heat transfer flux of about 58 W/m from the surface to the atmosphere.

Heat transfer from the surface to the atmosphere also includes 86.4 W/m from evaporation and plant transpiration, and 18.4 W/m from conduction and convection. Hence, the surface transfers heat to the atmosphere at an overall rate of about 123 W/m.

Data is from work published in 2009.

References:

"Climate and Earth’s Energy Budget", NASA Earth Observatory. 2009. — show Earth's energy flows being depicted as both energy flows and heat flows.

"Earth's Energy Budget", my NASA data, data from 2009 — shows energy flux values used in the current figure.