We analyze two multi-chord stellar occultations by Pluto observed on July 18th, 2012 and May 4th, 2013, and monitored respectively from five and six sites. They provide a total of fifteen light-curves, twelve of them being used for a simultaneous fit that uses a unique temperature profile, assuming a clear (no-haze) and pure N_2 atmosphere, but allowing for a possible pressure variation between the two dates. We find a solution that fits satisfactorily (i.e. within the noise level) all the twelve light-curves, providing atmospheric constraints between ~1,190 km (pressure ~ 11 \mubar) and ~ 1,450 km (pressure ~0.1 \mubar) from Pluto's center. Our main results are: (1) the best-fitting temperature profile shows a stratosphere with strong positive gradient between 1,190 km (at 36 K, 11 \mubar) and r = 1,215 km (6.0 \mubar), where a temperature maximum of 110 K is reached; above it is a mesosphere with negative thermal gradient of -0.2 K/km up to ~ 1,390 km (0.25 \mubar), where, the mesosphere connects itself to a more isothermal upper branch around 81 K; (2) the pressure shows a small (6 %) but significant increase (6-σ level) between the two dates; (3) without troposphere, Pluto's radius is found to be R_P = 1,190 +/- 5km. Allowing for a troposphere, R_P is constrained to lie between 1,168 and 1,195 km; (4) the currently measured CO abundance is too small to explain the mesospheric negative thermal gradient. Cooling by HCN is possible, but only if this species is largely saturated; Alternative explanations like zonal winds or vertical compositional variations of the atmosphere are unable to explain the observed mesospheric trend. ; Comment: 41 pages, 13 figures, 4 tables