In this study, we investigate heat current correlations between two edge states coupled through a constriction in the fractional quantum Hall regime at filling factor ν = 1/3. This configuration allows us to map the system onto an interacting Tomonaga-Luttinger liquid with a local impurity, where the interaction parameter takes the value κ = 1/2. This specific parameter value enables the application of the refermionization method. By solving the refermionized Hamiltonian, we compute the heat current and evaluate the finite-frequency heat auto- and cross-correlation functions. Our results reveal asymmetric behavior with frequency, corresponding to absorption and emission noise, respectively. Furthermore, we examine several limiting cases, including low- and high-temperature limits as well as strong- and weak-backscattering regimes. In the weak backscattering regime, the Lorenz number approaches 4L₀ at high voltage, suggesting a rescaling of the Wiedemann-Franz law due to interactions. A detailed study of the heat current fluctuations has made it possible to identify and derive expressions for the dominant contribution in the various regimes of interest, and to reveal the predominance of partition noise.