The selection of suitable parameters, by experimental or intuitive processes for snap-through actuation of a bimetallic actuator at a prescribed temperature is an extremely time-consuming task. This paper describes a new methodology for the optimization of a discrete action thermo-bimetallic actuator with a tongue. This methodology makes it possible to solve the optimization task with higher efficiency. The requirement is to find optimal parameters values so that the actuator will make a snap-through at a given temperature. The constrained optimization task was performed using an evolutional algorithm and surrogate modelling and this was coded in Matlab. Functional relationships between the criteria and parameters were not set explicitly, but they were calculated using finite element method, each simulation of which was performed in Abaqus