In our study, we develop a model for simulating fracturing processes in a poroelastic medium. The proposed approach combines the discrete fracture model enriched with contact plane mechanics. The model captures mechanical interactions of fractures and a deformable medium, fluid, and heat transfer in fractures and in a porous medium. Both effects of poroelasticity and thermoelasticity are accounted in our model. Mass and heat conservation equations are approximated by the finite volume method, and mechanical equilibrium equations are discretized by means of the Galerkin finite element approach. Two-dimensional grid facets between 3-dimensional finite elements are considered as possible fracture surfaces. Most of these facets are inactive from the beginning and are activated throughout the simulation. A fracture propagation criterion, based on Irwin's approach, is verified on each nonlinear iteration. When the criterion is satisfied, additional contact elements are added into finite element and discrete fracture model formulations respectively. The proposed approach allows modeling of existing natural and artificially created fractures within one framework. The model is tested on single- and multiple-phase fluid flow examples for both isothermal and thermal conditions and verified against existing semianalytical solutions. The applicability of the approach is demonstrated on an example of practical interests where a sector model of an oil reservoir is simulated with different injection and production regimes.