Fluid flow and heat transfer in a microstructure may depart from the traditional behavior due to the scale effect, and its velocity slip and temperature jump will occur at the fluid-solid interface. A molecular dynamics model of coupled fluid flow and heat transfer in rough nanochannels is developed to investigate the effect of surface roughness on nanoscale fluid flow and heat transfer, as well as velocity slip and temperature jump at the fluid-solid interface. The fluid microscopic structure, velocity and temperature distributions, interfacial velocity slip and temperature jump in a rough nanochannel are evaluated and compared with the corresponding smooth nanochannel. Effects of solid-liquid interaction and wall stiffness on the velocity slip and temperature jump are analyzed. Results indicate that the velocity of the fluid flow under an external force in a nanochannel in a bulk region is of a parabolic distribution, and the viscous dissipation due to shear flow induces the fourth-order temperature profile in the nanochannel. And the velocity slip and temperature jump will occur at the fluid-solid interface. The presence of roughness may introduce an extra viscous dissipation in shear flow, leading to a reduction of overall velocity and an increase in temperature in the nanochannel when compared with the smooth nanochannel. In addition, the degree of velocity slip and temperature jump at a rough liquid-solid interface is smaller than that at a smooth interface. In particular, the increase in fluid-solid interaction strength and reduction in wall stiffness will lead to a small velocity slip and temperature jump.