  Studies of thermal transport in long-range (LR)interacting systems are
currently particularly challenging. The main difficulties lie in the choice of
boundary conditions and the definition of heat current when driving systems in
an out-of-equilibrium state by the usual thermal reservoirs. Here, by employing
a reverse type of thermal baths that can overcome such difficulties, we reveal
the intrinsic features of thermal transport underlying a LR interacting
Fermi-Pasta-Ulam chain. We find that under an appropriate range value of LR
exponent $\sigma =2$, while a \emph{nonballistic} power-law length ($L$)
divergence of thermal conductivity $\kappa$, i.e., $\kappa \sim L^{\alpha}$
still persists, its scaling exponent $\alpha \simeq 0.7$ can be much larger
than the usual predictions in short-range interacting systems. The underlying
mechanism is related to the system's new heat diffusion process, weaker
nonintegrability and peculiar dynamics of traveling discrete breathers. Our
results shed light on searching for low-dimensional materials supporting higher
thermal conductivity by involving appropriate LR interactions.
