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A comparison of the filled temperature contours for the first solution (using the original mesh and first-order discretization) and the last solution (using an adapted mesh and second-order discretization) clearly indicates that the latter is much less diffusive. While first-order discretization is the default scheme in ANSYS FLUENT, it is good practice to use your first-order solution as a starting guess for a calculation that uses a higher-order discretization scheme and, optionally, an adapted mesh.
In this problem, the flow field is decoupled from temperature, since all properties are constant. For such cases, it is more efficient to compute the flow-field solution first (i.e., without solving the energy equation) and then solve for energy (i.e., without solving the flow equations). You will use the Equations dialog box to turn the solution of the equations on and off during such a procedure.