A rotatable antenna apparatus has a fixed unit for attachment of the apparatus to an external structure, and a rotatable unit mounted on the fixed unit for rotation relative to the fixed unit. The rotatable unit comprises both an antenna assembly and processing circuitry coupled to the antenna assembly for performing signal processing operations. The apparatus further includes a thermally conductive shaft connected to the rotatable unit and located for rotation within the fixed unit, and a thermally conductive coupling structure to conduct heat from one or more heat generating components of the processing circuitry into the thermally conductive shaft. A heat sink within the fixed unit is thermally coupled to the thermally conductive shaft to draw heat away from the thermally conductive shaft. This provides an efficient mechanism for removing heat from the rotatable unit, whilst still allowing the rotatable unit to be sealed against external environmental conditions.