As the diversity of exoplanets continues to grow, it is important to revisit assumptions about habitability and classical habitable zone definitions. In this work, we introduce an expanded 'temperate' zone, defined by instellation fluxes in the range $0.1< S/\mathrm{S}_{\oplus }< 5$, thus encompassing a broader range of potentially habitable worlds. We also introduce the TEMPOS survey, which aims to produce a catalogue of precise radii for temperate planets orbiting M dwarfs with $T_\mathrm{eff}\le 3400\,$ K. This work reports the discovery and characterization of two planets in this temperate regime orbiting mid-type M dwarfs: TOI-6716 b, a $R_\mathrm{b}=0.98\pm 0.07\, \mathrm{R}_{\oplus }$ planet orbiting its M4 host star ($R_\star =0.231\, \pm 0.015\mathrm{R}\, _\odot$, $M_\star =0.223\pm 0.011\, \mathrm{M}\, _\odot$, $T_\mathrm{eff}=3110\pm 80\, \mathrm{K}$) with a period $P=4.7185898^{+0.0000054}_{-0.0000041}\, \mathrm{d}$, and TOI-7384 b, a $R_\mathrm{b}=3.56\pm 0.21\, \mathrm{R}_{\oplus }$ planet orbiting an M4 ($R_\star =0.319\, \pm 0.018\mathrm{R}\, _\odot$, $M_\star =0.318\pm 0.016\, \mathrm{M}\, _\odot$, $T_\mathrm{eff}=3185\pm 75\, \mathrm{K}$) star every $P=6.2340258^{+0.0000034}_{-0.0000036}\, \mathrm{d}$. The radii of TOI-6716 b and TOI-7384 b have precisions of 6.8 per cent and 5.9 per cent, respectively. We validate these planets with multiband ground-based photometric observations, high-resolution imaging, and statistical analyses. We find these planets to have instellation fluxes close to the inner (hotter) edge of the temperate zone, with $S_\mathrm{b}=4.4\pm 1.1\, \mathrm{S}_{\oplus }$ and $S_\mathrm{b}=4.9\pm 1.1\, \mathrm{S}_{\oplus }$ for TOI-6716 b and TOI-7384 b, respectively. Also, with a predicted transmission spectroscopy metric similar to the TRAPPIST-1 planets, TOI-6716 b is likely to be a good rocky-world James Webb Space Telescope target, should it have retained its atmosphere.