  This study analyzes the temperature fluctuations in incompressible
homogeneous isotropic turbulence through the finite scale Lyapunov analysis of
the relative motion between two fluid particles. The analysis provides an
explanation of the mechanism of the thermal energy cascade, leads to the
closure of the Corrsin equation, and describes the statistics of the
longitudinal temperature derivative through the Lyapunov theory of the local
deformation and the thermal energy equation. The results here obtained show
that, in the case of self-similarity, the temperature spectrum exhibits the
scaling laws $\kappa^n$, with $n \approx{-5/3}$, ${-1}$ and ${-17/3} \div
-11/3$ depending upon the flow regime. These results are in agreement with the
theoretical arguments of Obukhov--Corrsin and Batchelor and with the numerical
simulations and experiments known from the literature. The PDF of the
longitudinal temperature derivative is found to be a non--gaussian distribution
function with null skewness, whose intermittency rises with the Taylor scale
P\'eclet number. This study applies also to any passive scalar which exhibits
diffusivity.
