This study focuses on the influences of natural convection on the temperature distribution in a compact thermoacoustic coaxial heat pump. The behaviour of this device is quite consistent with results of Rott's linear theory of thermoacoustics, but early measurements reveal a non-uniformity of the temperature along the transverse dimension of the core, as well as nonlinear axial temperature profiles. To investigate the contribution of natural convection on these temperature distributions, a hanging system allowing the device to be rotated around 2 axes is implemented. For each configuration, temperature at various locations in the thermoacoustic core is recorded using an array of 3 by 5 thermocouples, and heat balance in the core is performed. All the experimental data are analysed to provide a better understanding of the heat flows in the device.