  We develop a theory to probe the effect of non-equilibrium
fluctuation-induced forces on the size of a polymer confined between two
horizontal thermally conductive plates subject to a constant temperature
gradient, $\nabla T$. We assume that (a) the solvent is good and (b) the
distance between the plates is large so that in the absence of a thermal
gradient the polymer is a coil whose size scales with the number of monomers as
$N^{\nu}$, with $\nu \approx 0.6$. We predict that above a critical temperature
gradient, $\nabla T_c \sim N^{-\frac{5}{4}}$, favorable attractive
monomer-monomer interaction due to Giant Casimir Force (GCF) overcomes the
chain conformational entropy, resulting in a coil-globule transition. The
long-ranged GCF-induced interactions between monomers, arising from thermal
fluctuations in non-equilibrium steady state, depend on the thermodynamic
properties of the fluid. Our predictions can be verified using light-scattering
experiments with polymers, such as polystyrene or polyisoprene in organic
solvents (neopentane) in which GCF is attractive.
