Hey Peter, how old is your motor? I have a 95 70hp yammie.
If it goes into limp mode it should shake and carry on when you try and increase throttle.
When I first got mine, second hand it did similar to yours on a run back through the heads on the shoalhaven, not a place you want to loose power. Motor dropped all power before getting its breath and having another go. Found one spark plug badly eroded. Replaced plugs and problem never returned.
Rick is probably right, but I would start with the easiest items first.
Plugs , leads, filters. If the boat is new to you but you have no service history it's probably not a bad idea anyway.
Let us know how you get on.
Also, I did seize mine a few years later when a blade of the impeller inexplicably decided to let go, it had similar Simptoms. Heat up, get tight then when idled cool down, loosen up again and repeat until I shut it down at the ramp and it locked solid. Hope this isn't the case for you.