Experiments with drug-induced epilepsy in rat brains and epileptic human brain region reveal that focal cooling can suppress epileptic discharges without affecting the brain's normal neurological function. Findings suggest a viable treatment for intractable epilepsy cases via an implantable cooling device. However, precise mechanisms by which cooling suppresses epileptic discharges are still not clearly understood. Cooling experiments in vitro presented evidence of reduction in neurotransmitter release from presynaptic terminals and loss of dendritic spines at post-synaptic terminals offering a possible synaptic mechanism. We show that termination of epileptic discharges is possible by introducing a homogeneous temperature factor in a neural mass model which attenuates the post-synaptic impulse responses of the neuronal populations. This result however may be expected since such attenuation leads to reduced post-synaptic potential and when the effect on inhibitory interneurons is less than on excitatory interneurons, frequency of firing of pyramidal cells is consequently reduced. While this is observed in cooling experiments in vitro, experiments in vivo exhibit persistent discharges during cooling but suppressed in magnitude. This leads us to conjecture that reduction in the frequency of discharges may be compensated through intrinsic excitability mechanisms. Such compensatory mechanism is modelled using a reciprocal temperature factor in the firing response function in the neural mass model. We demonstrate that the complete model can reproduce attenuation of both magnitude and frequency of epileptic discharges during cooling. The compensatory mechanism suggests that cooling lowers the average and the variance of the distribution of threshold potential of firing across the population. Bifurcation study with respect to the temperature parameters of the model reveals how heterogeneous response of epileptic discharges to cooling (termination or suppression only) is exhibited. Possibility of differential temperature effects on post-synaptic potential generation of different populations is also explored.