Enhanced oil recovery (EOR) processes sometimes involve wellbore heating by means of electromagnetic radiation, electrical heating, or steam injection. When a wellbore is heated in tar sands and bituminous reservoirs, many thermo-physical properties of the bitumen and rock matrix can change significantly and thereby alter the fluids and heat flow behaviour. This paper presents the development of a mathematical formulation that describes the flow behaviours of heat and fluids around a wellbore during the initial period of heating in tar sands and bituminous reservoirs. The model shows that the transient temperature distribution is not affected significantly by convection. However, the pressure distribution exhibits an abnormally high pressure build-up resulting from the relative thermal expansion of in situ bitumen in the region where the temperature is slightly higher than the reservoir temperature. The mathematical model can be used to obtain predictions of pressure-temperature distributions around heated wellbores, well communication time required in the steam assisted gravity drainage (SAGD) process, and well stimulation and absolute permeability improvement resulting from progressive shear dilation in low permeability bitumen and tar sand reservoirs.