Air quality models help in developing relationships between the amount of pollutant released into the ambient atmosphere by a source and the corresponding incremental contribution in the atmospheric concentration. Of the various dispersion models, the heavy gas models help in predicting the concentrations due to release of gases heavier than air and the risks associated with the increased concentrations. Several differences exist among the various models developed to study the heavy-gas dispersion phenomena. These differences mainly arise because of the varied treatment given to physical processes involved in the dispersion mechanism. One of these processes, which have not been fully considered in many of the existing models, is the effect of ground heating on the movement of a cloud under windy conditions. In this study, the box model developed by Kunsch and Fannelop (J. Hazard. Mater. 43 (1995) 169) is extended to incorporate variable air entrainment on the dispersion of a heavy gas cloud spreading in a channel under windy conditions. The air entrainment was assumed to be proportional to the cloud frontal velocity. The semi-analytical equations developed were then solved by numerical methods to provide a heavy gas cloud dispersion profile. The popular Runge-Kutta fourth order technique was adopted to solve the differential equations numerically. The model was applied on a cold cloud released instantaneously and the results indicated that the model behavior follows closely the expected dispersion trends and observed cloud characteristics reported in a laboratory study. The trial run carried out in order to model the scenario of no heat transfer, by equating the source temperature to the ambient temperature, followed variations observed in the field. The analysis of cloud behavior indicated that the cloud length is strongly influenced by source density and initial cloud temperature.