I'm thinking that nothing was very wrong when you decided to service the water pump. So problems appearing after this service probably have to do with possible mistakes. I would not be amazed at all if it is just a matter of the key not installed on the driveshaft when setting the impeller in place.
I presume that you used a barrel or muffs. As far as I remember a 1958 10 horse does not have a peehole so you do not really know if the water made it all the way up. It could just be a matter of the lower unit not deep enough in the barrel and/or not enough water going up to the engine. Or simply having installed the impeller while turning the driveshaft counter clockwise There may well be a blockage of pieces of impeller rubber debris clogging the passages.
I would remove the lower unit again make sure everything was installed the proper way. Then remove the thermostat to see if it works or maybe replace it. and while that housing is off put a hose with good water pressure in that space and run the water backward down the system to flush it out, also flush the copper tubing that goes up to the engine.
Once you eliminated all those possibilities, you must reinstall the lower unit. Even with a little ten horse like that it is often groping in the dark so you should lay that engine at least flat or slanted slightly upside down and with the help of a flashlight make sure that the tube goes properly in the cooling inlet with the rubber grommets in the right place. and then carefully reassemble the lower unit and you should be good to go.
The amazing thing about these little 10 horse engines is the amount of punishment they can take without getting a lot of damage
