I have a 1997 FLHRI The bike wants to rev and runs hot

It has a history of it. Your best bet it to take it to a Yamaha dealer and get it tuned up. It is likely to be a carburetor issue not closing properly.

https://www.google.com/search?q=2004+Yz450f+high+revs+at+idle

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It sounds as if a throttle cable or choke cable is either sticking or badly routed . Most bikes rev high at cold start then the revs should decrease as the engine warms up. I would check the throttle and choke cables first make sure they lubricated and operate smoothly and especially with the throttle cable if you open it slowly does it return immediately you take your hand away. It should almost snap shut. I would also check out the pilot air screw in the carb these get clogged with debris from the petrol over time. Before you take the pilot air screw out turn it clockwise into the carb and note how many turns it takes until it stops (do not over tighten this screw) be very gentle when you do this. Check your user manual to see if the turns in you found match the turns out in the manual. Also make sure the tick over (idle) adjuster screw is set correctly your bike should idle at approx 1,200 to 1,300 RPM when hot. My Yamaha 125 is 1,300 RPM my Suzy 650 about the same.

rev limit is set at around 4000 rpm

Just twist the throttle (LOL)! Assuming you have EFI and you are talking about changing the rev limit you will need a laptop, screaming eagle race tuner software and the connector block unique for your bike. These can be bought online or at your local H-D dealer. You can then change many parameters, including air/fuel ratio at particular rpm's as well as the rev limiter setting. There are other ways to do this, but this it what the manufacturer recommends.

If you need further help, reach me via phone at https://www.6ya.com/expert/david_1f7d1c330c9dd97d

You have to adjust the idle cold,and hot. Warm the bbike up,and with the air filter housing off,look at the bottom right? of the backing plate,and there will be a small hole. There is a small torx bit screw in that hole that you will need to turn to adjust the hot idle. Dont quote me,but i think its a t20 or t25 torx bit.

There are adjustments on carbs for low speed air intake (air mixture screw)find out factory settings and reset that mixture.Sounds to me like those adjustments are out of sink.If so the bike will run very bad from idle to about 1/4 throttle then run great from there up to full throttle.this definitly sounds like carb problem.

Does it rev high when started cold or hot? If it does it either hot or cold, check the throttle position sensor on throttle body. If that is not bad, then check the automatic choke sensor.

OK.... firstly change the fuel cap, the tank needs to be vented correctly so pressure will equalise. Normally a rich fuel concentration will cause the engine to die not run high. From what your telling me it sounds like the throttle cables are not adjusted properly, if they are too tight the rpm's will not come back to idle. if this is the case you might be able to twist the throttle the opposite direction to lower the revs at idle. For the excess fuel problem, it could be what you say about the fuel cap, another thing will be the Needle and Seat might need changing or the float levels are not adjusted correctly. Whilst your there fit a good inline fuel filter, it will stop problems in the future.

check your spark plug if it burns ok. if it burns white its ok, also clean your carburator and the air cleaner after that start the engine again. if it does not change the problem is youre cdi unit.

it might be a sticky frotal