Aims. We investigate the photometric characteristics of a sample of intermediate-luminosity red transients (ILRTs), a class of elusive objects with peak luminosity between that of classical novae and standard supernovae. Our goal is to provide a stepping stone in the path to reveal the physical origin of such events, thanks to the analysis of the datasets collected. Methods. We present the multi-wavelength photometric follow-up of four ILRTs, namely NGC 300 2008OT-1, AT 2019abn, AT 2019ahd, and AT 2019udc. Through the analysis and modelling of their spectral energy distribution and bolometric light curves, we inferred the physical parameters associated with these transients. Results. All four objects display a single-peaked light curve which ends in a linear decline in magnitudes at late phases. A flux excess with respect to a single blackbody emission is detected in the infrared domain for three objects in our sample, a few months after maximum. This feature, commonly found in ILRTs, is interpreted as a sign of dust formation. Mid-infrared monitoring of NGC 300 2008OT-1 761 days after maximum allowed us to infer the presence of ∼10-3-10-5 M⊙ of dust, depending on the chemical composition and the grain size adopted. The late-time decline of the bolometric light curves of the considered ILRTs is shallower than expected for 56Ni decay, hence requiring an additional powering mechanism. James Webb Space Telescope observations of AT 2019abn prove that the object has faded below its progenitor luminosity in the mid-infrared domain, five years after its peak. Together with the disappearance of NGC 300 2008OT-1 in Spitzer images seven years after its discovery, this supports the terminal explosion scenario for ILRTs. With a simple semi-analytical model we tried to reproduce the observed bolometric light curves in the context of a few solar masses ejected at few 103 km s-1 and enshrouded in an optically thick circumstellar medium.