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 ± 0.0000018 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 ± 0.30 M_⊕, and radius, R_b = 1.264 ± 0.050 R_⊕. 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 ± 0.91 M_⊕, and orbital period, P_c = 15.509 ± 0.033 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.