  A framework for studying the effect of the coupling to the heat bath in
models exhibiting anomalous heat conduction is described. The framework is
applied to the harmonic chain with momentum exchange model where the
non-trivial temperature profile is calculated. In this approach one first uses
the hydrodynamic (HD) equations to calculate the equilibrium current-current
correlation function in large but finite chains, explicitly taking into account
the BCs resulting from the coupling to the heat reservoirs. Making use of a
linear response relation, the anomalous conductivity exponent $\alpha$ and an
integral equation for the temperature profile are obtained. The temperature
profile is found to be singular at the boundaries with an exponent which varies
continuously with the coupling to the heat reservoirs expressed by the BCs. In
addition, the relation between the harmonic chain and a system of
noninteracting L{\'e}vy walkers is made explicit, where different BCs of the
chain correspond to different reflection coefficients of the L{\'e}vy
particles.
