Since the phase change in SMA-based devices such as actuators is accompanied by a significant heat exchange with the surroundings, different concepts to heat/cool SMAs have been proposed in the literature. Most of these concepts require the analysis of a multilayered (e.g., "sandwich"-type) structure where the SMA layer is placed between layers with another material. In this paper we propose a mathematical model and an efficient numerical method for this analysis. Although our approach can be applied to a wide range of different designs of multilayered actuators, the basic idea of the model construction is explained in this paper for a specific design based on the introduction of semiconductor "heat pump" modules into the device and the Peltier effect for the heat exchange. The dynamics of thermomechanical fields is studied with a coupled system of PDEs based on conservation laws. The system, supplemented by constitutive relationships in the Falk form, is reduced to a differential-algebraic (DA) model and solved with an effective DA solver developed in our previous works. Numerical results on thermomechanical behaviour of SMA components in multilayered actuators are presented.