We study the heat transport along an edge state of a two-dimensional electron gas in the quantum Hall regime, in contact to two reservoirs at different temperatures. We consider two exactly solvable models for the edge state coupled to the reservoirs. The first one corresponds to filling $ν=1$ and tunneling coupling to the reservoirs. The second one corresponds to integer or fractional filling of the sequence $ν=1/m$ (with $m$ odd), and capacitive coupling to the reservoirs. In both cases we solve the problem by means of non-equilibrium Green function formalism. We show that heat propagates chirally along the edge in the two setups. We identify two temperature regimes, defined by $Δ$, the mean level spacing of the edge. At low temperatures, $TΔ$, finite-size effects become irrelevant, but the heat transport strongly depends on the strength of the edge-reservoir interactions, in both cases. The thermal conductance for tunneling coupling grows linearly with $T$, whereas for the capacitive case it saturates to a value that depends on the coupling strengths and the filling factors of the edge and the contacts. ; Comment: 15 pages, 5 figures