In this study, a magnetorheological (MR) damper is experimentally characterized and investigations on the temperature developed during the operation of the damper, its effect on the damper hysteresis are carried out. The increase in temperature at higher input current consequently reduces the damper peak force and energy dissipation, thus altering its hysteretic behaviour. This hysteresis, with dependency on temperature, is modelled using a Gaussian kernel based support vector regression (SVR) model. Three methods, namely particle swarm optimization (PSO)-SVR, gravitational search algorithm (GSA)-SVR and a newly proposed PSOGSA-SVR are studied for finding the optimal hyper parameters for effective modelling of the damper. From the experimental training and testing datasets, four different models of the damper depending on the input frequency are obtained using all three methods and evaluated with five performance indices. The results indicate that the proposed PSOGSA-SVR is an effective non-parametric modelling tool for predicting the hysteresis of the MR damper with temperature effect.