The polar bear and several other Arctic mammals use fur composed of hollow-core fibers to survive in extremely cold environments. Here, we use finite element analysis to elucidate the role that the hollow core plays in regulating thermal transport. Specifically, we establish a three-dimensional model of a textile based on fibers with various core diameters and study transverse heat transport. First, these simulations revealed that textiles based on hollow-core fibers conduct significantly less heat than their solid-core counterparts with fibers with a core-to-fiber diameter ratio of 0.95, reducing thermal transport by 33%. In addition to this decrease in thermal transport, the mass per area of textiles is substantially reduced by making them hollow core. This led us to consider the performance of multi-layer textiles and to find that four-layer hollow-core textiles can exhibit a four-fold decrease in heat flux relative to single-layer solid-core textiles with the same mass per area. Taken together, these simulations show that hollow-core fibers are well suited for thermal insulation applications in which gravimetric thermal insulation is a priority.