Many end users have taken laser alignment equipment and “checked” alignments on equipment that has been running satisfactorily,  and very often with vibration data that falls well within alarm thresholds, only to find the alignment out of normal alignment tolerances. In this instance, the vibration data should be the determining factor. If the equipment is running well, leave it alone. It would however be a very good practice to keep this alignment data and use it in the future for the intentional misalignment of this particular machine. It is quite possible that the machine had in fact been deliberately misaligned when cold and stopped to compensate for positional changes that occur due to thermal growth or dynamic load shifts.