We consider a theory for local thermal non-equilibrium in a porous medium where the solid and fluid components may have different temperatures. A priori estimates are derived for a solution to the governing partial differential equations and these are employed in an analysis of continuous dependence and of convergence. It is shown that the solution depends continuously on changes in the coefficient governing the interaction between the fluid and solid temperatures. This coefficient is key to the theory since this is where the equations are coupled. We also prove a convergence result demonstrating that the solution converges appropriately as the coupling coefficient vanishes.