Thermocouples are one of the most widely used temperature measurement devices due to their low cost, ease of manufacture and robustness. However, their robustness is obtained at the expense of limited sensor bandwidth. Consequently, in many applications signal compensation techniques are needed to recover the true temperature from the attenuated measurements. This, is turn, necessitates in situ thermocouple characterisation. Recently the authors proposed a novel characterisation technique based on the cross-relation method of blind deconvolution applied to the output of two thermocouples simultaneously measuring the same temperature. This offers a number of advantages over competing methods including low estimation variance and no need for a priori knowledge of the time constant ratio. A weakness of the proposed method is that it yields biased estimates in the presence of measurement noise. In this paper we propose the inclusion of a signal conditioning step in the characterisation algorithm to improve the robustness to noise. The enhanced performance of the resulting algorithm is demonstrated using both simulated and experimental data.