Different analytical models have been developed over the past few decades for evaluating thermal contact conductance (TCC or h), but they are limited to particular cases/applications and are based on too many simplifying assumptions. It is difficult to isolate and study the independent effects of different influencing parameters of TCC experimentally. Therefore, to estimate the TCC, it is essential to model the rough surface and do the heat transfer analysis. In this work the effect of asperity height and the number of discrete contact points on TCC is studied. The contact between a conforming smooth-flat and rough surface is considered to evaluate TCC at the interface. A Gaussian distribution with zero mean and standard deviation equal to the root mean square (RMS) value of the surface roughness is considered for generating the asperity height distribution of the required rough surface. Two surfaces with RMS values of 5 µm and 3 µm roughness are considered. To study the effect of number of contacting asperities, the roughness is kept constant at 5 µm and the number of contacting asperities is taken as 11 and 51. Effect of air conduction on heat transfer across the interface is also studied for all the cases. A steady state heat diffusion equation is solved along with the appropriate boundary conditions to achieve the same. A qualitative analysis of the effect of TCC is presented by comparing the top surface temperature of the considered physical domain for different cases of contact. It is found that TCC increases with the number of contacting asperities and decreases with increase in surface roughness.