We present broad-band photometry of 30 planetary transits of the ultra-hot Jupiter KELT-16b, 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 four years, and searched for transit time variations. We found no evidence for a period change, suggesting a lower limit for orbital decay at 8 Myr, with a lower limit on the reduced tidal quality factor of $Q^{prime}_{star}>(1.9 pm 0.8) times 10^5$ with $95%$ 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-16b has a phase offset of $25.25 pm 14.03$ $^{circ}$E, a day- and night-side brightness temperature of $3190 pm 61$ K and $2668 pm 56$ K, 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 planets atmosphere, the chemical composition of which is preferably oxygen-rich rather than carbon-rich.
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