  We develop a model for the power spectrum of unresolved clusters of galaxies
arising from the thermal Sunyaev-Zeldovich (tSZ) effect. The model is based on
a'universal' gas pressure profile constrained by X-ray observations and
includes a parameter to describe departures from self-similar evolution. The
model is consistent with recent Planck observations of the tSZ effect for X-ray
clusters with redshifts z<1 and reproduces the low amplitude for the tSZ
inferred from recent ground based observations. By adjusting two free
parameters, we are able to reproduce the tSZ power spectra from recent
numerical simulations to an accuracy that is well within theoretical
uncertainties. Our model provides a simple, empirically motivated tSZ template
that may be useful for the analysis of new experiments such as Planck.
