Solid-state microcoolers offer an attractive way to solve some of the problems related to temperature stabilisation and control, not only in optoelectronic and microelectronic applications, but also in biological applications where specimens require cooling. One of the important parameters of these coolers is their transient response or their cut-off frequency. We studied how this parameter is influenced by material properties (e.g., substrate and superlattice layer thermal diffusivities), and by geometrical factors (e.g., microcooler cross sectional area or thickness). Our models are based on a modified Thermal Quadrupole Method, which only takes the Peltier effect into account; the reason behind the modification is that the Peltier and Joule effects are uncorrelated in the frequency domain, so their contributions can be studied separately. The thermophysical properties of the microcooler are assumed to be temperature independent. The effect of the top side heat leakage on the performance of the microcooler is also presented.