  Temperature contrasts and magnetic field strengths of sunspot umbrae broadly
follow the thermal-magnetic relationship obtained from magnetohydrostatic
equilibrium. Using a compilation of recent observations, especially in
molecular bands, of temperature contrasts of starspots in cool stars, and a
grid of Kurucz stellar model atmospheres constructed to cover layers of
sub-surface convection zone, we examine how the above relationship scales with
effective temperature T_{eff}, surface gravity g and the associated changes in
opacity of stellar photospheric gas. We calculate expected field strengths in
starpots and find that a given relative reduction in temperatures (or the same
darkness contrasts) yield increasing field strengths against decreasing T_{eff}
due to a combination of pressure and opacity variations against T_{eff}.
