We characterized the broad-band X-ray spectra of Swift J1745-26 during the decay of the 2013 outburst using INTEGRAL ISGRI, JEM-X and Swift XRT. The X-ray evolution is compared to the evolution in optical and radio. We fit the X- ray spectra with phenomenological and Comptonization models. We discuss possible scenarios for the physical origin of a ~50 day flare observed both in optical and X- rays ~170 days after the peak of the outburst. We conclude that it is a result of enhanced mass accretion in response to an earlier heating event. We characterized the evolution in the hard X-ray band and showed that for the joint ISGRI-XRT fits, the e-folding energy decreased from 350 keV to 130 keV, while the energy where the exponential cut-off starts increased from 75 keV to 112 keV as the decay progressed.We investigated the claim that high energy cut-offs disappear with the compact jet turning on during outburst decays, and showed that spectra taken with HEXTE on RXTE provide insufficient quality to characterize cut-offs during the decay for typical hard X-ray fluxes. Long INTEGRAL monitoring observations are required to understand the relation between the compact jet formation and hard X-ray behavior. We found that for the entire decay (including the flare), the X-ray spectra are consistent with thermal Comptonization, but a jet synchrotron origin cannot be ruled out. ; Comment: Accepted for publication by MNRAS