Engine noise Motor has noise in the top end , But only when cold and at 2000 rpm. It sounds like cam chain , But it goes away when it warms up.

It could be piston gudgeon pin

sounds to me like a heat sheild is loose on the fire wall or under the car

Sounds to me like the cam bearings are gone as that is where you get your oil pressure . most of those have to be pressed in after the motor is pulled out and tore down and going that deep i would go ahead and rebuild the whole motor while you have it out.

Check carb balance as this can cause primary drive gear lash as these are straight cut gears

Bikes rattle quite often, can you be more clear of where this noise may be coming from?

No oil chain is behind the clutch I think. It's either the clutch (does the noise go away when you pull in the lever?) or the cam chain.

I do not know what your mileage is but if you are over 110,000 in a DOHC then a cam chain is in order unless it has already been done. when you do it get a kit as the are guides, sprockets, and a tensioner needed as well. when you are putting it back together do the serpentine belt tensioner and the dog bone motor mounts. generally a cam chain sounds more like loud whirr than click. sticky valves click, but that generally goes away as the engine warms up. a/c clutch could make a click cutting in and out if the system is dry and there is nothing to compress. have you tried this in park with the hood open and someone else hitting the gas pedal to hit the magic rpm? you might see something attending the click or get some better idea as to exact location.

it can either be a worn tensioner or need for a valve adjustment. if you rev the engine and noise goes away, you need a new cam chain tensioner. if the noise remains or gets worse when you rev it up, you need a valve adjustment and should replac the tensioner anyway. 36,000 miles on the motor is definitely mileage for an adjustment if it's never had one.

Take all of the belts off for a short run at idle. If the sound goes away it is pulley related, spin each pulley and listen for bearing noise, also check for play at this time.

If the noise does not go away when the motor is driving no accessories you have a more serious problem.

top end noise usaully the sign of needing a valve adjustment. some occassions just need a new cam chain tensioner. when you rev up engine rpms, if the sound goes away that means your tensioner is bad and not adjusting properly. if the noise gets worse then it's time to let a technician do his thing.