An analytic approximate procedure, called optimal homotopy asymptotic method (OHAM) is considered for the solution of strongly nonlinear differential equations arising in heat transfer. Two particular applications are chosen: convecting-radiating cooling of a lumped system with variable specific heat and fins with temperature dependent surface heat flux. The effectiveness of the method, which is independent of the small parameter, is investigated by comparing the results obtained with the exact and the results already present in the literature. (c) 2012 Elsevier Ltd. All rights reserved.