Estimating the thermal state within a glacier and at the bed is important for many glaciological applications. Examples include oldest-ice reconnaissance, ice-sheet dynamics and more. However, widespread measurements of thermal profiles in glaciers are not available simply because currently temperatures can only be measured in drill holes. We propose using radar data, particularly attenuation, to overcome this limitation and constrain the thermal state away from drill holes. First, the problem will be formulated in a Bayesian framework, outlining each of the key steps. After describing the methodology, we will show the results of a case study in Dome Fuji, East Antarctica. Finally, we discuss how this approach can be applied to other parts of Antarctica.