  In the interaction of high-power laser beams with solid density plasma there
are a number of mechanisms that generate strong magnetic fields. Such fields
subsequently inhibit or redirect electron flows, but can themselves be advected
by heat fluxes, resulting in complex interplay between thermal transport and
magnetic fields.We show that for heating by multiple laser spots reconnection
of magnetic field lines can occur, mediated by these heat fluxes, using a fully
implicit 2D Vlasov-Fokker-Planck code. Under such conditions, the reconnection
rate is dictated by heat flows rather than Alfv\`enic flows. We find that this
mechanism is only relevant in a high $\beta$ plasma. However, the Hall
parameter $\omega_c \tau_{ei}$ can be large so that thermal transport is
strongly modified by these magnetic fields, which can impact longer time scale
temperature homogeneity and ion dynamics in the system.
