Evolution of heating radius (solid line) and cooling radius with (dashed line) and without (dot‐dashed line) heating correction in unit of the virial radius for halos with mass 10¹², 10¹³, 10¹⁴, and 10¹⁵ M_⊙ today (beginning from the top left plot; mass increases clockwise). Thick lines are for zero metallicity while thin lines are for solar metallicity. Note that the 10¹² M_⊙ halo plot does not have a heating curve because in that case cooling dominates heating at the virial radius.