Solid oxide fuel cells (SOFC) generate electricity cleanly, efficiently and quietly. There has been much effort in commercialising planar and large tubular SOFCs in the past two decades. Some research has involved modelling the mass, thermal and electrical energy flows in SOFC stack designs. Due to increased thermo-mechanical strength, a minitubular configuration offers quicker start up than planar designs, higher power densities than large tubular designs, and the potential for easier sealing. A stack housing design that bundled the small tubular fuel cells inside a three-way heat exchanger was proposed. Effluent fuel from the fuel cells was combusted to form an integrated burner. The air required is supplied by natural convection generated from the exhaust and hot gasses flowing up a flue (chimney). Experimental trials were done with a fabricated test rig (verification cell) to assess the stack housing design when operated with hydrogen-air. Temperature profiles data were collected to investigate the effect of varying fuel flow rate, chimney dimensions, and insulation. Code was written for the finite element program ANSYS® to model the verification cell. This included a simple model for the flame in the verification cell. Robustness of the model was investigated by varying software settings, and comparing predicted temperature profiles with measured temperature profiles for varying fuel flow rates, chimney dimensions, and insulation. The verification cell operated successfully on hydrogen-air but the temperature was not high or uniform enough to support a fuel cell stack. Using insulation increased temperatures and produced a more uniform temperature distribution. Increasing flue length increased temperatures marginally but increasing flue width decreased temperatures by 10%. A simple model for the hydrogen flame was used as the heat source in the verification cell to predict temperature profiles for a given set of flow rates and operating conditions. Temperature profiles could be correlated with flow rate within 10% of actual data for the air and exhaust manifolds, but accuracy was not translated for other fuel flow rates. The benefits and drawbacks of the ANSYS® program for modelling the SOFC stack are discussed and recommendations on further research given.