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 = 100;
  
krok[{t_, T_}] = {t + Δt, 
          T + derT[T]*Δt};
pocatek = {0, 100};
Res = 
        NestWhileList[krok, pocatek, #1[[2]] > 30 &, 
          1];
  
tepl[t_] = Interpolation[Res, InterpolationOrder -> 5][
          t];
tmax = 
        Last[Res] // First;
  
eqn = derT[T[t]] == T'[t];
poc = T[0] == 100;
teeepl[t_] = 
        T[t] /. NDSolve[{eqn, poc}, 
              T[t], {t, 0, tmax}][[1]];
Plot[{tepl[t], teeepl[t]}, {t, 0, tmax}, 
        AxesLabel -> {"t[s]", "T[°C]"}, 
        PlotStyle -> {{Hue[0.65], Thickness[0.008]}, {Hue[0. ], 
              Thickness[0.008]}}];
Plot[tepl[t] - teeepl[t], {t, 0, tmax}, 
          AxesLabel -> {"t[s]", "T[°C]"}, 
          PlotStyle -> {Hue[0.65], Thickness[0.008]}, 
          PlotRange -> All];;