Resorting to what is termed informational statistical thermodynamics, namely, the microscopic foundations of irreversible thermodynamics in terms of the nonequilibrium informational ensemble, the problem of heat transport in a system of bosons is considered. In a truncated description of the macroscopic state of the system we derive the equations of evolution appropriate for an extended hydrodynamiclike approach. We particularize the analysis to those macrovariables corresponding to energy density and energy flux whose equations of evolution are nonlinear generalizations of Mori-Langevin equations. We arrive at an equation of propagation of thermal waves with damping. The thermal excitations are of the type of second sound. The different transport coefficients (like velocity of propagation, thermal diffusivity, relaxation times, etc.) receive an interpretation at the microscopic mechano-statistical level. We derive the limiting conditions to be imposed to recover Fourier's theory as an approximation.54547384747