Context. The underlying scenario of the formation and evolution of galaxy triplets is still uncertain. Mergers of galaxies in isolated triplets give us the opportunity to study the already complex merging process, with minimal contamination of other environmental effects that potentially allow and accelerate galaxy transitions from active star-forming to passive galaxies. Aims. The merging system SIT 45 (UGC 12589) is one of 315 systems in the SDSS-based catalogue of Isolated Triplets (SIT); it is an unusual isolated galaxy triplet, consisting of three merging late-type galaxies. The main aims of this work are to study the dynamical evolution and star formation history (SFH) of SIT 45, as well as its dependence on its local and large-scale environment. Methods. To study its dynamics, parameters such as the velocity dispersion (σv), the harmonic radius (RH), the crossing time (H0tc), and the virial mass (Mvir), along with the compactness of the triplet (S) were considered. To investigate the possible dependence of these dynamical parameters on the environment, the tidal force Q parameters (both local and large-scale) and the projected local density (ηk) were used. To constrain the SFH, we used CIGALE to fit its observed spectral energy distribution using multiwavelength data from the ultraviolet to the infrared. Results. SIT 45 is one of the most compact triplets in the SIT, and it is also more compact than triplets in other samples. According to its SFH, SIT 45 presents star formation, where the galaxies also present recent (∼200 Myr) star formation increase, indicating that this activity may have been triggered by the interaction. Its dynamical configuration suggests that the system is highly evolved in comparison to the SIT. However, this is not expected for systems composed of star-forming late-type galaxies, based on observations in compact groups. Conclusions. We conclude that SIT 45 is a system of three interacting galaxies that are evolving within the same dark matter halo; its compact configuration is a consequence of the ongoing interaction rather than being due to a long-term evolution (as suggested from its H0tc value). We consider two scenarios for the present configuration of the triplet, one where one of the members is a tidal galaxy, and another where this galaxy arrives to the system after the interaction. Both scenarios need further exploration. The isolated triplet SIT 45 is therefore an ideal system to study short timescale mechanisms (∼108 yr), such as starbursts triggered by interactions which are more frequent at higher redshift.