Temperature-induced changes in the propagation of electromagnetic surface waves guided by the planar interface of a temperature-sensitive isotropic material (namely, InSb) and a temperature-insensitive anisotropic material were investigated theoretically in the terahertz frequency regime. Two types of anisotropic partnering material were considered: (i) a homogeneous material and (ii) a periodically nonhomogeneous material. As the temperature increases, the isotropic partnering material is transformed from a weakly dissipative dielectric material to a plasmonic material. As a consequence, the surface waves change from Dyakonov surface waves to surface-plasmon-polariton waves for case (i), and change from Dyakonov-Tamm surface waves to surfaceplasmon-polariton waves for case (ii). Numerical investigations demonstrated that dramatic changes in the numbers of propagating Dyakonov or Dyakonov-Tamm surface waves, their angular existence domains, their propagation constants, and their decay constants, could arise from modest changes in temperature.