Fluid flow and heat transfer in a nanochannel may depart from the traditional behavior due to the scale effect, and the velocity slip and temperature jump at the fluid-solid interface must be taken into account. A lot of papers about fluid flows in nanochannels with the same wettability at two surfaces have been published. It is necessary to investigate fluid flow and heat transfer in nanochannels with the asymmetric wettability by the molecular dynamics method. The fluid velocity and temperature distributions, interfacial velocity slip and temperature jump in a rough nanochannel are evaluated. The effects of asymmetric wettability on the velocity slip, temperature jump and internal fluid heat transfer are analyzed. The 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, but the parabolic distribution is not centrosymmetric because of the centrosymmetric density profile. The difference in density distribution can affect the fluid flow. Viscous dissipation due to shear flow will increase the fluid temperature. The range that is affected by the interaction between solid and liquid is small. So the wettability of the cold wall hardly affects the velocity of the fluid near the hot wall, and the slip velocity is almost constant. At this time, the negative slip will take place at the fluid-solid interface near the hot wall. But the velocity of the fluid near the cold wall comes up with the increasing hydrophobicity of the cold wall, and the slip velocity increases. The temperature jump on both sides of interface increases with the increasing hydrophobicity of the cold wall, but the degree of temperature jump at a liquid-cold solid interface is higher than that at a liquid-hot solid interface. Then the fluid temperature near the cold wall gradually exceeds the fluid temperature near the hot wall. The internal heat flow of the fluid will be reversed. The inverted temperature profile of the fluid will appear. The inverted temperature profile becomes more obvious when the degree of asymmetric wettability increases.