Cellobiohydrolases (CBHs) break down cellulose sequentially by sliding along the crystal surface with a single cellulose strand threaded through the catalytic tunnel of the enzyme. This so-called processive mechanism relies on a complex pattern of enzyme-substrate interactions, which need to be addressed in molecular descriptions of processivity and its driving forces. Here, we have used titration calorimetry to study interactions of cellooligosaccharides (COS) and a catalytically deficient variant (E212Q) of the enzyme Cel7A from Trichoderma reesei. This enzyme has about 10 glucopyranose sub sites in the catalytic tunnel, and using COS ligands with a degree of polymerization (DP) from 2 to 8, different regions of the tunnel could be probed. For COS ligands with DP of 2-3 the binding constants were around 105 M-1, and for longer ligands (DP 5-8) this value was about 107 M-1. Within each of these groups, we did not find increased affinity as the ligands got longer and potentially filled more sub sites. On the contrary, we found a small but consistent affinity loss as DP rose from 6 to 8; particularly at the higher investigated temperatures. Other thermodynamic functions (ΔH, ΔS and ΔCp) decreased monotonously with both temperature and DP. Combined interpretation of these thermodynamic results and previously published structural data allowed assessment of an affinity profile along the length axis of the active tunnel.