  The irradiation of protoplanetary discs by central stars is the main heating
mechanism for discs, resulting in their flared geometric structure. In a series
of papers, we investigate the deep links between 2D self-consistent disc
structure and planetary migration in irradiated discs, focusing particularly on
those around M stars. In this first paper, we analyse the thermal structure of
discs that are irradiated by an M star by solving the radiative transfer
equation by means of a Monte Carlo code. Our simulations of irradiated
hydrostatic discs are realistic and self-consistent in that they include dust
settling with multiple grain sizes (N=15), the gravitational force of an
embedded planet on the disc, and the presence of a dead zone (a region with
very low levels of turbulence) within it. We show that dust settling drives the
temperature of the mid-plane from an $r^{-3/5}$ distribution (well mixed dust
models) toward an $r^{-3/4}$. The dead zone, meanwhile, leaves a dusty wall at
its outer edge because dust settling in this region is enhanced compared to the
active turbulent disc at larger disc radii. The disc heating produced by this
irradiated wall provides a positive gradient region of the temperature in the
dead zone in front of the wall. This is crucially important for slowing
planetary migration because Lindblad torques are inversely proportional to the
disc temperature. Furthermore, we show that low turbulence of the dead zone is
self-consistently induced by dust settling, resulting in the Kelvin-Helmholtz
instability (KHI). We show that the strength of turbulence arising from the KHI
in the dead zone is $\alpha=10^{-5}$.
