The quasar-type blazar 3C 454.3 underwent a phase of high activity in summer and autumn 2007, which was intensively monitored in the radio-to-optical bands by the Whole Earth Blazar Telescope (WEBT). The gamma-ray satellite AGILE detected this source first in late July, and then in November-December 2007. In this letter we present the multifrequency data collected by the WEBT and collaborators during the second AGILE observing period, complemented by a few contemporaneous data from UVOT onboard the Swift satellite. The aim is to trace in detail the behaviour of the synchrotron emission from the blazar jet, and to investigate the contribution from the thermal emission component. Optical data from about twenty telescopes have been homogeneously calibrated and carefully assembled to construct an R-band light curve containing about 1340 data points in 42 days. This extremely well-sampled optical light curve allows us to follow the dramatic flux variability of the source in detail. In addition, we show radio-to-UV spectral energy distributions (SEDs) at different epochs, which represent different brightness levels. In the considered period, the source varied by 2.6 mag in a couple of weeks in the R band. Many episodes of fast (i.e. intranight) variability were observed, most notably on December 12, when a flux increase of about 1.1 mag in 1.5 hours was detected, followed by a steep decrease of about 1.2 mag in 1 hour. The contribution by the thermal component is difficult to assess, due to the uncertainties in the Galactic, and possibly also intrinsic, extinction in the UV band. However, polynomial fitting of radio-to-UV SEDs reveals an increasing spectral bending going towards fainter states, suggesting a UV excess likely due to the thermal emission from the accretion disc.Read less <