Thermal stress is one of the main factors affecting the degradation rate of solid oxide fuel cell (SOFC) stacks. In order to mitigate the possibility of fatal thermal stress, stack temperatures and the corresponding thermal gradients need to be continuously controlled during operation. Due to the fact that in future commercial applications the use of temperature sensors embedded within the stack is impractical, the use of estimators appears to be a viable option. In this paper we present an efficient and consistent approach to data-driven design of the estimator for maximum and minimum stack temperatures intended (i) to be of high precision, (ii) to be simple to implement on conventional platforms like programmable logic controllers, and (iii) to maintain reliability in spite of degradation processes. By careful application of subspace identification, supported by physical arguments, we derive a simple estimator structure capable of producing estimates with 3% error irrespective of the evolving stack degradation. The degradation drift is handled without any explicit modelling. The approach is experimentally validated on a 10 kW SOFC system. (C) 2016 Elsevier B.V. All rights reserved.