  We present the confirmation and characterisation of GJ 3473 b (G 50--16,
TOI-488.01), a hot Earth-sized planet orbiting an M4 dwarf star, whose
transiting signal ($P=1.1980035\pm0.0000018\mathrm{\,d}$) was first detected by
the Transiting Exoplanet Survey Satellite (TESS). Through a joint modelling of
follow-up radial velocity observations with CARMENES, IRD, and HARPS together
with extensive ground-based photometric follow-up observations with LCOGT,
MuSCAT, and MuSCAT2, we determined a precise planetary mass, $M_b =
1.86\pm0.30\,\mathrm{M_\oplus},$ and radius, $R_b =
{1.264\pm0.050}\,\mathrm{R_\oplus}$. Additionally, we report the discovery of a
second, temperate, non-transiting planet in the system, GJ 3473 c, which has a
minimum mass, $M_c \sin{i} = {7.41\pm0.91}\,\mathrm{M_\oplus,}$ and orbital
period, $P_c={15.509\pm0.033}\,\mathrm{d}$. The inner planet of the system, GJ
3473 b, is one of the hottest transiting Earth-sized planets known thus far,
accompanied by a dynamical mass measurement, which makes it a particularly
attractive target for thermal emission spectroscopy.
