Suppose a body cools from 70°C to 60°C and then again cools from 60°C to 50°C. If surrounding temperature is 30°C then the rate of heat loss from 70° to 60°C would be different to that from 60° to 50°C.
Since the temperature difference between the surrounding and the body is less we can write rate of cooling :-
$$-\frac{\mathrm dT}{\mathrm dt} =k(T-T_0),$$
where $T_0$ is the surrounding temperature which remains constant and $T$ is the temperature of the body at any instant $t$.
Since $T$ does not remain constant ($-\mathrm dT/\mathrm dt$) varies, my question is that if the temperature difference between the body and surrounding and not negligible, then we apply Stefan's law to calculate the initial rate of heat loss. In the Stefan's law, we have to take the difference between body's absolute temperature and surrounding temperature, so if the body is continuously losing heat do we have to always take the starting Temperature of the body at which it was kept or we have change that temperature continuously?
For example, if the initial temperature of the body is $T_1$ and after some time it cools and temperature becomes $T_2$, so the initial heat loss will be $Aeρ(T_1-T')$; then will the rate of heat loss changes when the temperature of the body becomes $T_2$ and rate changes to :- $[Aeρ(T_2-T')]$
