Bianchi Type I tilted cosmological model for barotropic perfect fluid distribution with heat conduction is investigated.To get the deterministic solution, we have assumed barotropic condition p = γ ∈ ,0 < γ < 1, p being isotropic pressure, ∈ the matter density and a supplementary condition between metric potentials A, B, C as A = (BC)n where n is the constant. To get the model in terms of cosmic time, we have also discussed some special cases. The physical aspects of the model are also discussed.