Transient free convection from a heated surface immersed in a cold ambient is investigated using scale analysis. The heated plate is our model for the heat exchangers in a natural draft dry cooling tower. The scale analysis results led to a timescale for initiation of the plumes. Furthermore, a model is developed to study the near-wall free convection which allows the prediction of plume extension and merging process. Both the normal and lateral components of the fluid velocity are expressed as functions of the Prandtl and Rayleigh number. Expressions are proposed to predict the plume size and spacing in the lateral direction. Results are then successfully compared with independent experimental data available in the literature.