In a previous paper of the author, the notion of global equivalence between two deformable thermoelastic bodies B and 13' was introduced. This equivalence is understood in the sense that a global thermokinetic process for B is admissible (in the sense of Coleman and Noll) if and only if its counterpart for B', according to a suitable bijective correspondence k between B and
B'i
, also is admissible. In this case, B and B' are said to be globally k-equivalent. Global k-equivalence does not imply piecewise k-equivalence, that is, the global equivalence of arbitrary k-corresponding subbodies of B and B'. Here we present two maximality theorems of global equivalence for a rigid heat-conducting body B: one in the thermodynamic theory with no heat sources and the other in the thermodynamic theory with heat supply. By these theorems, given the rigid heat-conducting body B referred to its configuration -% in both the theories we characterize the constitutive equations for all rigid heat conductors B' that have a configuration A' with '(13') = '5(B) and are globally k-equivalent to B for k = t-y oy.
