By most standards, that is not a very large gearbox. The gearbox manufacturer should have provided tables with expected thermal growth and horizontal movement. I did not understand if this is a gear increaser or a reducer. I did not understand if it was single helical or double helical. You did not specify if this was a sleeve bearing or roller bearing arrangement. If you do not have the manufacturer's projected thermal growth, then I would calculate the growth. Since gearboxes tend to be foot mounted and warm all the way to the base plate, they typically grow much more than an electric motor. The motor will probably grow vertically less than 0.005”. The motor manufacturer should be able to provide a projected thermal growth of the motor.
I would measure from the base plate to the shaft centerline. I would calculate the thermal growth from ambient temperature up to running temperature (about 150 °F for many of my comparable gearboxes). I would measure the center to center distance between the pinion and bull-gear and do the same calculation. The top of the gearbox will get wider when it heats up. In addition, the gears will tend to spread apart forcing the two shafts to the outer side of the bearing clearance. I would expect the drive gear to move to the outside by one half of the calculated horizontal thermal growth plus about one half of the driven gear bearing clearance. Some will tell you that the gearbox should be doweled under the pinion and that all or most of the movement will be in the direction of the bull-gear. Direct measurement of gearbox movement has convinced me that this is not correct. The dowel pins position the gearbox, but the hold-down bolts keep it in this position.
When rolling the alignment, it is better if you can turn the shafts from the motor side in the direction or normal rotation. If this is a gear reducer with a small pinion, you have to be especially careful of this. If the rotation for turning the alignment tools lifts the pinion up in its clearance, it is difficult to predict where it will end up. Most gearboxes of this sort are down-mesh. If this is an up-mesh box, then I would consider rotating it in the direction opposite of normal rotation so that you are always forcing the pinion down to the bottom of the bearing. You can try it both ways to see which one gives better repeatability. If this is a gear reducer with sleeve bearings on the pinion, it is preferred to perform the alignment uncoupled. The weight of the coupling and the stiffness of the coupling can lift the smaller pinion out of the bottom of the bearing clearances and give a false result.
If you have to run the unit unloaded, then the motor and the gearbox will not get up to full temperature. You will be running with a poorer alignment during this time. But for a motor and gearbox this size, I would not expect any problem. You should circulate the oil system with the oil heated up to at least 100 °F prior to startup to minimize this initial misalignment. You may also want to reduce the thermal offsets slightly to reduce the cold misalignment. I usually round these values down slightly so that I pass through the ideal alignment during heat-up and end up a little bit on the other side at normal running conditions.
If you could describe the gear type, bearing type, coupling type and whether this is an increaser or reducer, you may get more usefully comments.
Johnny Pellin