1984 35HP Stalling

[dunvillekid]

I have a 1984 35HP that I just bought this year. Installed new Plugs and cleaned Carb. Engine starts and runs..For how long is the question. I have had it run at trolling speed for an hour plus with no problem. I have taken it out and run it at varying speeds on several occasions and it stalls, maybe after 2 minutes of warming up maybe after 15 minutes of cruising. Whenever it does stall, it will not fire back up immediately. It seems if you let it sit for a while it will eventually fire up and run for a while longer. It does appear to be circulating water, but I noticed the other day while trying to diagnose the problem in the yard it appeared to have stopped. Appears to be getting fuel ok. Tried starting with starting fluid after a couple of the stalls and no luck. When it dies, it does not sputter out, its just like turning the key off. Would a faulty/insuficient water pump cause this?

Scratching my head at a drift....