Rockets are the most convenient way to reach space. Rockets accelerate the molecules formed as a result of combustion in the rocket through a nozzle and throws it out, thus creating thrust. The thrust produced by energized and accelerated hot gas expelling through nozzle. Rockets are categorized by ways of putting energy to these particles. A rocket motor is an example of the energy transformation system. This energy transformation can be done by accelerating particle using an electric field, nuclear energy, or heating particles by chemical reactions. With high safety and reliability, hybrid rocket engines as an example of chemical rockets can be better alternative of bi-liquid propulsion systems in terms of development and production cost. The aim of this study is to investigate the nozzle behavior in a small-scale and low-cost hybrid rocket engine in oxygen rich environment under thermal motor is designed, developed, and tested. Theoretically the conjugate gradient method with adjoin problem for function estimation iterative technique is used to solve the Inverse Heat Conduction Problem (IHCP) to estimate heat flux and internal wall temperature of the nozzle. The convective heat transfer coefficient is calculated using Bartz equation. The results are compared with the test data.