A superconducting metallic film bolometer in contactwith thermal bath of temperature T 0, is biased by a (i)constant current $I_{\mathrm{b} }$ , or by (ii) the constantvoltage $U_{\mathrm{b}}$ . The absorption of the time-dependentpower of a phonon beam W(t) elevates temperature of the film to $T(t)>T_{\mathrm{0}}$ . The thermal contact of the bolometer withthe environment is characterized by the thermal conductance G,and it depends on $[T^{n}(t)-T_{\mathrm{0}}^{n}]$ ( $n=4{-}6$ ). Forboth above methods of bias, we derive ordinarynonautonomous nonlinear differential equations of the first order.These equations are numerically solved. The knowledge of W(t)allows one to calculate (i) $U_{\mathrm{b} }(t)$ or (ii) $I_{\mathrm{b}}(t)$ . The inverse problem of calculation of W(t)from known (i) $U_{\mathrm{b}}(t)$ or (ii) $I_{\mathrm{b}}(t)$ isalso solved. Using W(t) calculated in computer experiments, weobtained the bolometer signal, and compared it with results ofreal experiments performed on GaAs in which $I_{\mathrm{b}}$ isfixed, and U is measured. Comparison of calculated results withresults obtained for the linearized model shows that thenonlinearity is essential for the correct description of metallicsuperconducting film bolometer response.