We predict how turbulence generated temperature fluctuations propagate from the fluid regions into the adjacent walls.Within the RANS approach this is achieved by extending the transport equations for temperature variance and its dissipation rate acrossthe solid walls which bound the flow region. The results of recent DNS studies of conjugate heat transfer under fully developedconditions in straight channels have been used to develop and optimize the model. Simulations of 1D fully developed channel flow(friction Reynolds number 150, Prandtl numbers 0.71 and 7) with heated solid wall are carried out and compared with DNS data, usingan existing four-equation model proposed by Craft et al.[4] as a starting point. The transport equations for the two thermal parameters,temperature variance and its dissipation rate, are optimized by focusing on the decay of these two parameters in the solid region, usingboundary values at the interface between the solid and fluid regions provided by DNS. Then a physically consistent and numericallystable set of interface conditions are developed to account for the jump in the value of temperature variance dissipation rate across thesolid-fluid interface, caused by the different material thermal properties. Subsequent conjugate heat transfer simulations show that theproposed model is able to predict the correct distribution of the temperature variance within both the fluid and solid regions, for theentire range of thermal diffusivity and conductivity ratios between the fluid and solid regions and also for both fluid Prandtl numbers