It is shown that strong T_c-inhomogeneity of high temperature superconductors (HTSC) leads to a modification of the mechanism of the thermodynamic noise in these materials. In spatially inhomogeneous materials, along with classical thermodynamic noise associated with random heat exchange between superconductor and its environment, there exists an excess thermodynamic noise associated with heat exchange inside the superconductor. Besides, due to inhomogeneity, the effective volume which makes a dominant contribution to the fluctuations of sample resistance can be far less than the total volume of the sample. Using a simple model we derive the expression for the spectral density of resistance noise for a thin superconducting film. It is shown that spatial T_c-inhomogeneity can lead to a substantial enhancement of noise.