Three‐point upper and lower bounds on the effective thermal expansion coefficient and specific heats of statistically isotropic suspensions of mutually impenetrable spheres are computed for the first time. The three‐point bounds depend upon the microstructure via a three‐point spatial correlation function of the medium. Both equisized and multisized spheres are considered, and hence the effect of polydispersivity in sphere size on the thermoelastic properties is determined. For reasons of mathematical analogy, the results of this study for the thermal expansion coefficient translate immediately into equivalent results for the hygroscopic expansion coefficient.