There has to be a temperature difference between the receiving tank (cooler) and the supply tank, for LIQUID CO2 to transfer. Yes, the temperature difference will affect how much liquid CO2 transfers. Care needs to be taken not to overcharge the receiving tank. At high fill levels, the pressure/temp ratio can go exponential.
The only way to measure the fill is by weight. At some point, we went through all of this on the forum and determined the safe fill level for the 113/114. Not sure if it's possible to search for that.. it was some time ago. There are some charts that show the relationship between temp and pressure that's good to review.
with digital scales so inexpensive, there's no reason not to get one that can accept the weight of a 114. I got one that goes up to 30 pounds so it's not necessary to remove the action from the stock, although that can help with balancing on the scale. Using a scale is the only real way of answering your question about it making any difference between 10deg and 25 deg pre-chill temp.
What I found handy is to attach the fill tank, leave the gun uncocked so that the hammer sits on the exhaust valve and keeps it open, turn on the supply tank slowly so that CO2 is coming out of the muzzle. Turn supply tank off. Gun is now chilled. Cock the gun. Turn on supply tank. Then off. Detach supply tank and weigh the gun. Additional weight from the tare weight is the amount of CO2 transferred.
Roll pins. They make roll-pin punches that have round projection that centers the punch on the roll-pin.