The quest for non-Abelian quasiparticles has inspired decades of experimental and theoretical efforts, where the scarcity of direct probes poses a key challenge. Among their clearest signatures is a thermal Hall conductance with quantized half-integer value in units of κ0=π2kB2T /3 h (T is temperature, h the Planck constant, kB the Boltzmann constant). Such values were recently observed in a quantum-Hall system and a magnetic insulator. We show that nontopological "thermal metal" phases that form due to quenched disorder may disguise as non-Abelian phases by well approximating the trademark quantized thermal Hall response. Remarkably, the quantization here improves with temperature, in contrast to fully gapped systems. We provide numerical evidence for this effect and discuss its possible implications for the aforementioned experiments.