  We calculate the dependence of heat capacity of a free standing thin membrane
on its thickness and temperature. A remarkable fact is that for a given
temperature there exists a minimum in the dependence of the heat capacity on
the thickness. The ratio of the heat capacity to its minimal value for a given
temperature is a universal function of the ratio of the thickness to its value
corresponding to the minimum. The minimal value of the heat capacitance for
given temperature is proportional to the temperature squared. Our analysis can
be used, in particular, for optimizing support membranes for microbolometers.
