In this work, we describe a new wavelike nonlinear heat conduction model aimed at implementing chiral thermal management and dynamic tunable chiral thermal emission on rotating conductors exposed to a chopped laser beam. We assume the existence of a rotational dynamical thermal Hall effect due to a self-induced out-of-equilibrium Barnett magnetic field, demonstrating that it allows for the transverse deviation of the harmonic heat flux and the modulation of the phase velocity of helical thermal waves propagating on the rotating metallic disks. We introduce a novel dynamic approach to thermoelectricity with complex valued thermal field dependent transport coefficients,deducing then a new dynamic chiral Thomson effect. We show that it is proportional to the angular velocity vector of the rotating disk, providing an estimate of its average Thomson voltage coefficient in the case of a ferromagnetic sample. We exploit then the laser-induced chiral Thomson electric field associated with a time-dependent Barnett magnetic field to enhance dynamic magnetic phase transitions and to tune time dependent Curie temperature fluctuations. We introduce finally a dynamic tunable chiral thermal emissivity dependent on a gauge breaking thermal Poynting vector, outlining its relevance for a novel rotational approach to chiral nonreciprocal photonics.