We have measured activity and substrate affinity of the thermostable cellobiohydrolase, Cel7A, from Rasamsonia emersonii over a broad range of temperatures. For the wild type enzyme, which does not have a Carbohydrate Binding Module (CBM), higher temperature only led to moderately increased activity against cellulose, and we ascribed this to a pronounced, temperature induced desorption of enzyme from the substrate surface. We also tested a high affinity variant of R. emersonii Cel7A with a linker and CBM from a related enzyme. At room temperature, the activity of the variant was similar to the wild type, but the variant was more accelerated by temperature and about two-fold faster around 70 degrees C. This better thermoactivation of the high-affinity variant could not be linked to differences in stability or the catalytic process, but coincided with less desorption as temperature increased. Based on these observations and earlier reports on moderate thermoactivation of cellulases, we suggest that better cellulolytic activity at industrially relevant temperatures may be attained by engineering improved substrate affinity into enzymes that already possess good thermostability.