The propagation of plane waves in infinite, three–dimensional, type–III thermoelastic media is investigated. Exact dispersion relation solutions are determined and several characterizations of the wavefield are examined. Low– and high–frequency asymptotic expressions are given, small–coupling limit results are derived, and special/limiting cases, including those corresponding to thermoelastic media of types II and I, are noted. Computational tools are used to illustrate the analytical findings and to study the effects of varying the physical parameters. Of the findings presented, the following are most significant: (i) the determination of critical values of the physical parameters and their impact on the wavefields; (ii) ascertaining that type–III media behave, essentially, like type–II (respectively, type–I) media with respect to low– (respectively, high–) frequency plane waves; (iii) establishing the Whitham stability of plane waves in type–III media; and (iv) the determination of the dispersion characteristics of type–III media.