In the rocket motor design, there arises an acute need for a method of thermal analysis that could be directly coupled with the stress analysis. To describe the included thermal gradients with sufficient accuracy. the heat transfer coefficient together with the initial and boundary conditions should be well defined. Three-dimensional axisymmetric finite element method that accounts for transient heating and material non-linearities is presented. A computer program based on the finite element technique was implemented to determine the temperature distribution across the walls at any time instant. In order to verify the validity of the method it was firstly applied to the analytically known case of a thick hollow cylinder heated by convection on its internal surface. The method was then applied to a submerged nozzle made of composite material. The comparison with the results obtained from a general purpose thermal code has proven the applicability of the method to real problems. Practical measurements were made on an 80 mm testing motor for the temperature-time variation at different points through the nozzle wall. Numerical calculations using the developed program showed satisfactory agreement with test data.