  Twisted bilayer graphene (TBLG) has recently emerged as a versatile platform
for studying a variety of exotic transport phenomena. Here, we present a
theoretical study of near-field thermal radiation between suspended TBLG with a
focus on the magic angle. Within the chirally symmetric continuum model, we
observe a suppressed heat flow when approaching the magic angle owing to a
reduced Drude weight, with greater suppressions at lower temperatures and
larger gap sizes. When the chemical potential lies in the energy gap near the
charge neutrality point, more than 100-fold heat-flow variation can be achieved
at 50 K within 0.25{\deg}of twist. By reducing the electron scattering rate,
the radiation spectrum near the magic angle dramatically narrows, leading to
over 10,000-fold of suppression. In addition, supported TBLG is briefly
considered to facilitate experimental measurement. With rationally tailored
substrates, the heat-flow contrast can still exceed 1000. We also discuss
lattice relaxation effect in terms of the interlayer coupling energy, finding
that a stronger coupling leads to a smaller heat-flow contrast and more
prominent multiband transport. Our results highlight the great potential of
magic-angle TBLG in thermal transport, especially for controlling thermal
radiation.
