The paper describes an adaptive p-version finite element approach for two-dimensional thermal problems. The adaptive concepts advocated in the present work for thermal analysis seek to effectively improve the quality of the thermal response by hierarchically enriching the current approximations so as to achieve the best solution for a given computational effort. In particular, the solution schemes utilize computed information or feedback based on a posteriori error estimators/indicators for automating and therein steering the process of adaptive p-refinement. For the two-dimensional thermal models presented, the refinements are of local nature and edge-by-edge refinement strategy is advocated. Numerical test problems which are of comparative nature validate the proposed concepts for applicability to two-dimensional thermal problems.