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The thermal design of stratospheric balloon payloads usually focuses on the cruise phase of the missions, that is, the floating altitude conditions. The ascent phase usually takes between 2 and 4 h, a very small period compared to the duration of the whole mission, which can last up to 4 weeks. However, during this phase payloads are subjected to very harsh conditions due mainly to the convective cooling that occurs as the balloon passes through the cold atmosphere, with minimum temperatures in the tropopause. The aim of this work is to study the thermal behaviour of a payload carried by a long duration balloon during the ascent phase. Its temperature has been calculated as a function of the altitude from sea level to floating conditions. To perform this analysis it has been assumed that the thermal interactions (convection and radiation) depend on the altitude, on the environmental conditions (which in turn depend also on the altitude) and on the temperature of the system itself. The results have been compared with the measurements taken during the SUNRISE test flight, launched in October 2007 by CSBF from Fort Sumner (New Mexico).