The current energy situation has placed demand on exploitation of energy resources such as in geothermal reservoirs. Adequate exploitation of geothermal energy potential requires detailed evaluation of temperature profile in the medium. This work has thus developed a model to achieve this. A model was developed based on the conservation of mass, momentum and energy.The governing equations were solved using Crank-Nicholson version of the finite difference technique. The software was designed using MATLAB 5.0, Visual Basic 6.0 and Microsoft Excel. The visual basic component provides a means for the user to input parameters for the simulation. MATLAB provides the main computation while Excel was used to display the results. The software was used to simulate hot water displacement in a porous medium. The results obtained showed that fluid injected from the side of the reservoir medium responds slowly to changes in temperature distribution than when injected from the bottom.