1990 Johnson GT100 Thermostat?

I have a 1990 Johnson GT100 on a 17' Cajun bass boat. The Engine is a little rough starting cold and takes a minute to get up to speed when cold. Once running the engine runs like a champ. The problem I'm having is when I slow down in the no wake zones and go at a very slow speed thru the idle zone for 15 or more minutes when I go to start it just kinda bogs down. If I put it in neutral and rev the engine for a minute you can hear it start to run better and better until its running the proper RPMS, you can then put it back in drive and it once again goes like a bat out of hell. I also found that if I go thru the no wake zones at a higher speed "making a wake but no more than most" the problem seems to be eliminated. I had a guy tell me that its probably my thermostat stuck open and when idling it cools the engine too much and when you go to take off on a cold engine it bogs. Anyone know if there is any truth to this? And if so how hard is a thermostat to replace in an outboard? Any help would be appreciated. I did by the way buy new plugs which did not help.
Thanks
David