I have a newly rebuilt Mercury 200 efi (3.0) and when I leave my boathouse, I idle for about 400 yards to the river channel. I then trim in and give it gas, and the engine just bogs at about 2000 rpm for about 1/4 mile before taking off with a good holeshot. It may run a little rough for the first 15 seconds and then runs great. I can fish all day without any other problems. One of my fair boat mechanics here suggested replacing the computer, but that is an expensive guess. Are there thermostats on these motors? Got any suggestions? Thanks

There are definitely thermostats, I would look at many other options before an ECU.
Get some one with a DDT or CDS to plug in and read to see what is going on.

I have checked the therms and they are ok..the plugs look good as well. I don't have a easily accessable boat mechanic close to me that have that kind of test equipment...

You checked their operating temperature?
It should run around 143-145 degrees F
Does it smoke a lot?
Any fuel/oil in the water?
Also when rereading your original post it is a 200EFI, that would be a 2.5L.
If it is a 225 or 250 it would be a 3.0L
The 200 uses NGK plugs either BU8H or BPZ8Hs-10 depending on model year.
The 225 uses Champion Q77CC plugs, if you have your info crossed it could be part of your problem.

Thanks for the help.
I didn't check the temp in the boiling water...(keep in mind it does this in hot or cold temps)
Does not smoke excessively
no fuel/oil in water
It is a 2.5, sorry
Plugs are BPZ8H-N-10

Wrong plugs.
The BPZ8HS-N-10 is an early and no longer used plug for the 3.0L.
What is your serial number.
Early 2.4/2.5 EFIs took BU8H, Then Came BUZ8H and finally BPZ8HS-10
Serial number will tell us what plug to look for.

How cold is your cold weather?
In South Florida where our water temperature rarely falls below 65 and can run in the low 90s in the summer, EFIs still need working thermostats to maintain proper low speed operating temps.
If the ECU thinks the motor is cold it will richen fuel mixture to prevent stalling.
As a result when the thermostats are partially open (which is usually the case) the motors smoke,foul plugs, Etc.
An easy way to check them is to run the motor on a flushete or in the water at idle for about 5 minutes and then check with a IR temp gun, $30 at Home Depot. Or even easier put a new set in. I think the stats are about $12.00 each. You can also buy a thermostat kit for that motor with 2 thermostats and 2 gaskets for less $$.

After we get your baseline right (plugs, temp, air mixture, and timing) then I highly advise running a "shock" treatment of Mercury Quickleen to get the inside cleaned up.

I use Quickleen with every tank of fuel in my boat and highly advise all of my clients to use it all the time.

Thanks for the advise. I found that I was wront..this is a 2.5 (ser# OT390545). The motor had HS-10 plugs in it and I replaced them last fall with N-10.
The water temp last fall when this started was 88. Lately, I have been running in 47 - 60 deg water. It doen't make sense that after the first run attempt of the day it bogs and then it runs great the rest of the day.
Additional info: A local racer installed a used 225 ecu on my motor for me to do a test run yesterday..it ran great although it was very cold outside and windy and I never got it past 4500 rpm. He swapped them back out before he left, but I didn't run it again..

After the motor runs hard for a while it will come up to temperature, than when you shut it off it will "heat soak" and actually become hotter.
Cold is when it will run rich.