  We consider the problem of heat diffusion in branched systems and networks on
the basis of a model described in terms of heat equation on metric graphs.
Using the explicit analytical solutions of the latter, evolution of the
temperature profile and heat flow on each branch are computed. Extension of the
study for nonlinear regime is considered using a nonlinear heat equation on
metric graphs. It is found that in nonlinear regime is more intensive than that
in linear case.
