By means of a mean-field model extended to include magnetovolumic effects we study the effect of external fields on the thermal response characterized either by the isothermal entropy change and/or the adiabatic temperature change. The model includes two different situations induced by the magnetovolumic coupling. (i) A first order para- ferromagnetic phase transition that entails a volume change. (ii) An inversion of the effective exchange interaction that promotes the occurrence of an antiferromagnetic phase at low temperatures. In both cases, we study the magneto- and baro-caloric effects as well as the corresponding cross caloric responses. By comparing the present theoretical results with available experimental data for several materials we conclude that the present thermodynamical model reproduces the general trends associated with the considered caloric and cross caloric responses.