The propeller has to be advanced properly up the taper on the shaft. How much? Depends on the temperature at time of installation - you don't want the prop coming loose when the water gets warm.
Keys should be a snug fit in the shaft, and loose in the propeller hub. You may not care if your key is loose in the shaft, but some folks do.
Std prop taper is 3/4" per foot, or 1:16. Some commercial installations have gone to 1:20, as well as eliminating the key and the nut! The propeller is forced on the taper using hydraulics (think 20,000 psi) with hydraulic pressure between the taper and the hub. When the hub is in place, pressure is removed and the hub grabs the taper. A sealing plate keeps sea water away from the end of the shaft. When it's time to remove the prop, hydraulics is pumped between the taper and the shaft & off comes the prop. Like magic.
Use of heat to get a prop on or off is no sin. Forcing a big propeller up the taper on a 20" shaft in January when the river is freezing over takes a lot of oomph, and if you run out of oomph before you get to your target advancement, warming the hub will help a lot! Just might get you home for supper instead of tomorrow's breakfast.
The use of hydraulics has changed propeller installation & removal a great deal. I remember the old days when the technique was a long wrench to the propeller nut and a dockside crane. One installation wasn't quite getting there, so a second crane was added. They came close to rolling the ship right off the keel blocks in the graving dock.