We investigate heat current fluctuations induced by a periodic train of Lorentzian-shaped pulses, carrying an integer number of electronic charges, in a Hong-Ou-Mandel (HOM) interferometer implemented in a quantum Hall bar in the Laughlin sequence. We demonstrate that the noise in this collisional experiment cannot be reproduced in a setup with an effective single drive, in contrast to what is observed in the charge noise case. Nevertheless, the simultaneous collision of two identical levitons always leads to a total suppression even for the HOM heat noise at all filling factors, despite the presence of emergent anyonic quasiparticle excitations in the fractional regime. Interestingly, the strong correlations characterizing the fractional phase are responsible for a remarkable oscillating pattern in the HOM heat noise, which is completely absent in the integer case. These oscillations may be related to the recently predicted crystallization of levitons in the fractional quantum Hall regime.