Simple methods are developed to predict temperatures of a satellite box during the launch stage. The box is mounted on the outer surface of a satellite and directly exposed to a space thermal environment for the time period from fairing jettison to separation. These simple methods involve solving a 1st order ordinary differential equation (ODE), simplified from the full governing equation when several assumptions are made. The existence of an analytical solution for the 1st order ODE is determined depending on the treatment of the time-dependent molecular heating term. Even for the case that the analytical solution is not available due to the time dependent term, the 1st order ODE can be solved by relatively simple numerical techniques. The temperature difference between two different approaches (analytical and numerical solutions) is relatively small (less than 1°C along the time line) when they are applied to the STSAT-I launch scenario. The present methods can be generally used as tools to quickly check whether a satellite box is safe against the space environment during the launch stage for the case that the detailed thermal analysis is not available.