Conduction is the transfer of energy through particle-particle collisions. It is important near to planetary surfaces, and in the upper atmospheres (where the mean free path through the atmosphere is long, and atoms will swap places rapidly). We define the rate of flow of heat as

where Q is the heat flux (with units of erg/s/cm²) and k_T is the thermal conductivity. The specific heat is the change in energy required to raise the temperature of one gram of mass by one degree Kelvin, keeping the pressure and volume constant. For m, the mass of a mole of molecules, in grams,

Conduction acts to transfer daytime sunlight from the surface layer down through the planet. The rate at which subsurface layers gain heat is then

Diurnal variations in temperature are strongest at the surface, and fall off exponentially with an e-folding scale length of c_o, of order 10 cm, with a phase lag (like tides). The peak temperature depends upon the distance of the planet from the Sun, while the low temperature depends also upon _rot (as conductivity depends upon temperature, the subsurface heat becomes trapped under the surface at night). For low thermal conductivity, the amplitude of the temperature variation is high but it does not penetrate deeply into the surface. When thermal conductivity is high, the amplitude of the temperature variation is smaller but penetrates deeper into the subsurface.

Note that collisions tend to equalize temperature distributions in atmospheres, producing isothermal profiles. This is incompatible with convection, and so an atmosphere tends to be dominated by different mechanisms of energy transport (conduction, convection, and radiation) at different heights.