The rate of cooling R with excess of temperature $\mathrm{\Delta }\theta$ varies according to the graph

For small temperature difference by Newton’s law of cooling 
Rate of cooling $\propto$ temperature difference. At high temperature by Stefan’s law.

$-\frac{\mathrm{dT}}{\mathrm{dt}}=\frac{\sigma \mathrm{A}}{\mathrm{ms}}\left({\theta }^4-{\theta }_0^4\right)$