cp = 4186;
m = 1;
α = 5;
ϵ = 0.8;
σ = 5.67*(10^(-8));
T0 = 20;
S = 0.06;
derT[
          T_] = -(S/(m*
                  cp)) (α*(T - 
                    T0) + ϵ*σ ((((T + 273.15))^4) - (((T0 + 273.15))^4)));

Δt = 10;
tmax = 10000;
n = (tmax/Δ)t;
krok[{t_, T_}] = {t + Δt, 
          T + derT[T]*Δt};
pocatek = {0, 100};
Res = 
        NestWhileList[krok, pocatek, #1[[2]] > 80 &, 
          1];
% // ListPlot[#, 
          AxesLabel -> {"t[s]", "T[°C]"}] &

% // ListPlot[#, 
          AxesLabel -> {"t[s]", "T[°C]"}] &