Direction of vibration of molecule with respect to transfer of heat

That would be really difficult to answer at individual molecule/atom level for conduction. If you are looking at conduction in metals, you should be worried more about movement of electrons which forms a major part of heat transfer and molecular vibration only a little. Having said that, the individual molecules may vibrate in directions other than the direction of heat transfer but the net movement will be in the direction of heat transfer (remember heat transfer is never in one direction - it is always 3 dimensional when you are looking at molecular level)