We aim to introduce surface reconstruction (SR) schemes to maintain the smooth equilibria, including the still-water and moving-water steady-state solutions, and guarantee the positivity of the water depth and the temperature of the Ripa system. In order to preserve the isobaric steady state, we introduce a provable positivity-preserving parameter, which is one of the main contributions of the current scheme. For preserving the moving-water steady states, we reconstruct the discharge and energy variables instead of the conservative variables. We also need to redefine the discretization of the source term for the moving-water equilibrium. Riemann problems with a step of the Ripa system are also particularly challenging for most numerical schemes. One reason is that the bed slope source term may become a singular measure at cell boundaries. We use the SR method to define local Riemann states, which are used to compute the numerical flux across the cell interface and discretize the source term of the Ripa system. The current scheme can preserve the still-water and moving-water steady states and guarantee the positivity of the water depth and the temperature. The current scheme easily extends to a two-dimensional Ripa system.