  Aims. Relativistic jets launched from active galactic nuclei accelerate up to
highly relativistic velocities within a few parsecs to tens of parsecs. The
precise way in which this process takes place is still under study. While
magnetic acceleration is known to be able to accelerate relativistic outflows,
little attention has been paid to the role of thermal acceleration. The latter
has been assumed to act only on compact regions, very close to the central
engine, and to become negligible on parsec scales. However, this holds under
the assumption of small internal energies as compared to the magnetic ones, and
whether this is true or what happens when we drop this assumption is currently
uncertain. Methods. We use a 2D relativistic magnetohydrodynamical code to
explore jet acceleration from sub-parsec to parsec scales. As initial
conditions for our models, we use observational constraints on jet properties
derived by means of very long baseline interferometry observations for a
Fanaroff Riley I radio galaxy, NGC\,315. We investigate the parameter space
established for this source and perform a number of simulations of
magnetically, thermally or kinetically dominated jets at injection, and compare
our results with the observed ones. Results. Our simulated jets show that when
thermal energy is comparable to or exceeds magnetic energy, thermal
acceleration becomes significant at parsec scales. This result has important
consequences, potentially extending the acceleration region far beyond the
collimation scales, as thermal acceleration can effectively operate within a
conically expanding jet. In all the models, we observe acceleration to be
driven by expansion, as expected. A number of our models allow us to reproduce
the acceleration and opening angles observed in NGC\,315. Finally, our results
indicate that disk-launched winds might play an important role in the jet
propagation.
