We present broad-band photometry of 30 planetary transits of the ultra-hot-Jupiter KELT-16 b, using five medium-class telescopes. The transits were monitored through standard B, V, R, I filters and four were simultaneously observed from different places, for a total of 36 new light curves. We used these new photometric data and those from the TESS space telescope to review the main physical properties of the KELT-16 planetary system. Our results agree with previous measurements but are more precise. We estimated the mid-transit times for each of these transits and combined them with others from the literature to obtain 69 epochs, with a time baseline extending over more than 4yr, and searched for transit time variations. We found no evidence for a period change, suggesting a lower limit for orbital decay at 8Myr, with a lower limit on the reduced tidal quality factor of Q'*>(1.9+/-0.8)x10^5^ with 95 per cent confidence. We built up an observational, low-resolution transmission spectrum of the planet, finding evidence of the presence of optical absorbers, although with a low significance. Using TESS data, we reconstructed the phase curve finding that KELT-16 b has a phase offset of 25.25+/-14.03{deg}E, a day- and night-side brightness temperature of 3190+/-61K and 2668+/-56K, respectively. Finally, we compared the flux ratio of the planet over its star at the TESS and Spitzer wavelengths with theoretical emission spectra, finding evidence of a temperature inversion in the planet's atmosphere, the chemical composition of which is preferably oxygen-rich rather than carbon-rich.