Re: 1996 120HP Hard To Start When It's Warm
Never assume the dealer perfomed ANY maintenance.
I would start with a compression check. This will give you a baseline as to your engine's overall health.
Then I would do things that don't require adjusting things first. De-carbon the engine. There's a sticky in the Repair and Maintenance parent forum.
Re-check the compression.
I'd then check/replace as needed: the fuel bulb, lines, and filters. There is a fuel pump diaphram that has a pretty short service life that I would replace as well. The diaphram is <$20 with shipping, includes the gasket and is very easy/quick to replace.
Once the fuel system is serviced, pump the fuel bulb with the engine in the running position. Verify the fuel bulb gets and stays hard. If fuel leaks out the intake or doesn't get firm, then you may have a worn float needle. This would require removal of the carbs and replacing the needles. The carb kits are <$20 per carb. It's very easy to remove the carbs and replace the needle/gaskets so don't fret if it needs to be done.
Replace the plugs and then perform a link and sync. This includes setting the idle mixture - for each carb, carb syncronization (making sure all the throttle butterflies open at the same time), and adjusting the timing. Lastly the idle speed.
And since you don't know the maintenance history, I'd go ahead and replace the water pump (impeller) and the thermostat. < $40 total.
And change the oil in the lower unit. - It's a simple drain and re-fill procedure. Be sure to use the proper Marine Outboard Lower Unit oil.
All this probably sounds like a lot, but in actuallity it should be done every season. - Maybe not replacing all the parts listed above, but the de-carbon, link and sync and lower unit oil replacement are seasonal maintenance.