Spectral data cubes of the interacting pair of galaxies NGC 2535 and NGC 2536 (the Arp 82 system) targeting bright emission lines in the visible band, obtained with the imaging Fourier transform spectrometer (iFTS) SITELLE attached to the Canada-France-Hawaii Telescope (CFHT), are presented. Analysis of Hα velocity maps reveals a bar in $\rm NGC\, 2536$. In $\rm NGC\, 2535$, we find strong non-circular motions outside the ocular ring, in the elliptical arc and tidal tails of $\rm NGC\, 2535$ and a misalignment between the kinematic and photometric position angles. We detect 155 HII region complexes in the interacting pair of galaxies and determine oxygen abundances for 66 of them using different calibrators. We find, regardless of the indicator used, that the oxygen abundance distribution in $\rm NGC\, 2536$ is shallow whereas, in $\rm NGC\, 2535$, it is best fitted by two slopes, the break occurring beyond the ocular ring. The inner slope is comparable to the one observed in isolated normal star-forming galaxies but the outer slope is shallow. We present a numerical simulation of the interaction that reproduces the observed tidal features, kinematics, and metallicity distribution, to investigate the effect of the interaction on the galaxies. The model indicates that the galaxies have undergone a close encounter, strongly prograde for the primary, and are half way in their course to a second close encounter.