The effects of temperature on a viscoelastic medium are important in considering the long-term design of a structure. Large-scale numerical computations associated with rock mechanics problems have required efficient and economical models for predicting temperature, stress, failure, and deformed structural configuration under various loading conditions. To meet this requirement, the complex dependence of the properties of geological materials on the time and temperature is modified to yield a reduced time scale as a function of time and temperature under the thermorheologically simple material (TSM) postulate. The thermorheologically linear concept is adopted in the finite element formulation by uncoupIing thermal and mechanical responses. The thermal responses, based on transient heat conduction or convective diffusion, are formulated by using the two-point recurrence scheme and the upwinding scheme, respectively. An incremental solution procedure with the implicit time stepping scheme is proposed for the solution of the thermoviscoelastic response. The proposed thermoviscoelastic solution algorithm is based on the uniaxial creep experimental data and the corresponding temperature shift functions, and is intended to minimize computational efforts by allowing the large time step size with stable solutions. A thermoelastic fracture formulation is also presented by introducing the degenerate quadratic isoparametric singular element for the thermally-induced line crack problems. The stress intensity factors are computed by use of the displacement method. Efficiency of the presented formulation and solution algorithm is initially demonstrated by comparison with other available solutions for a variety of problems. Subsequent field applications are made to simulate the post-burn and post-repose phases of an underground coal conversion (UCC) experiment and an in-situ nuclear waste disposal management problems. Time- and space-dependent temperature boundary conditions are used to simulate the chamber and radioactive heat source temperatures. The UCC chamber configuration is predicted by use of two-dimensional failure criteria using temperature-dependent mechanical properties of coal and overburden. A UCC fracture model is also evaluated by considering a thermoelastic elliptic cavity model with a linking channel demonstrating a possible channel closure in the active-burn stage. The presented FEM model simulations illustrate the feasibility of the developed formulations and numerical investigations in predicting the post-burn/post-repose temperature, displacement and stress responses. Recommendations for additional work on thermo-mechanical response formulation and associated computational technique are provided.