In this paper, I present a theoretical model of a relaxed cluster where the
temperature profile (hereafter TP) is structured by electronic thermal con
duction. Neglecting cooling and heating terms, the stationary energy conser
vation equation reduces to a second-order differential equation, the resolu
tion of which requires two boundary conditions, taken here as the inner rad
ius and the ratio between the inner and outer temperature. Thus a two-param
eter family of analytical models for the TP is obtained. Once these two con
stants are chosen, the TP has a fixed analytical expression, which reproduc
es nicely the observed 'universal' TP obtained by Markevitch et al. from AS
CA data. Using observed X-ray surface brightnesses for two hot clusters wit
h spatially resolved TP, the local polytropic index and the hot gas fractio
n profile are predicted and compared with ASCA observations (Markevitch et
al. 1999). Moreover, the total density profile derived from observed X-ray
surface brightness, hydrostatic equilibrium and the conduction-driven TP is
very well fitted by three analytical profiles found to describe the struct
ure of galactic or cluster haloes in numerical simulations of collisionless
matter. With the forthcoming availability of spatially resolved high-quali
ty spectroscopic data, the predicted shape of the TP (related to the temper
ature dependence of the heat flux for a collisionally ionized plasma) will
be tested directly against observations.