The effect of the thermal and contact resistances of ceramic plates plays a vital role in thermoelectric (TE) coolers with relatively short thermoelements, especially in TE microcoolers. Through first introducing equivalent impedances, like equivalent thermal conductance, electrical resistance etc., general performance formulae with familiar forms are developed to take into account the thermal contact effect on TE coolers. Then, two new approaches are presented to obtain simplified formulae at maxima for temperature difference, cooling rate and coefficient of performance. Compared numerically with real maximum cooling performances of TE coolers, simplified formulae are proved to be good approximations at small thermal contact resistance and not-too-short thermoelements. In addition, some errors in previous investigators' models are redressed.