  We study the thermal transport in a two-dimensional system with coexisting
superconducting (SC) and nematic orders. We analyze the nature of the
coexistence phase in a tight-binding square lattice where the nematic state is
modelled as a $d$-wave Pomeranchuk type instability and the feedback of the
symmetry breaking nematic state on the SC order is accounted for by mixing of
the $s$, $d$ paring interaction. The electronic thermal conductivity is
computed within the framework of Boltzmann kinetic theory where the impurity
scattering collision is treated in the both the Born and Unitary limits. We
present qualitative, analytical, and numerical results that show that the heat
transport properties of SC states emerging from a nematic background are quite
distinct and depend on the degree of anisotropy of the SC gap induced by
nematicity. We describe the influence of the Fermi surface topology, the van
Hove singularities, and the presence or absence of zero energy excitations in
the coexistence phase on the the low temperature behaviour of the thermal
conductivity. Our main conclusion is that the interplay of nematic and SC
orders has visible signatures in the thermal transport which can be used to
infer SC gap structure in the coexistence phase.
