I would get some muffs where water goes in both sides of lower unit for two reasons. First, when we bought our boat, we used a 30 gal tote because it was better to run the motor in, After 5min there was a huge oily mess that took me a half hour to clean up, I couldn't believe it, I thought this isn't going to work.
Second, we bought muffs ,the water goes in both sides. This eliminates any water height problems in the barrel or tote., or tank, less water waste..
Overheat is three things, impeller, get the correct impeller, Like was said above is keyway still in place, fins oriented for CM drive shaft, Did you test t-stat in hot water, or bad sensor, test in hot water,the motor WASN'T really overheating? If ok, we move on, make sure water tube is clear, run wire up tube, shine light up tube, pour lots of water down t-stat hole does it drain out water tube fast? Is plastic part on water pump housing where water tube goes in still in place or is it stuck on water tube like last overheat post, if water pump housing has the plastic adaptor in place for water tube to insert into, make sure the water tube goes into the plastic adaptor,when you install lower unit.