08 TE510 cut off when hot now will not idle

Backstory: I went on a 400 mile ride and halfway thru when I came to ilde the bike would cut off. If I kept the rpms up it ran great. I rode it twice after that and same problem but only when it had been running for 20 min or so. After researching the problem determined it must be a coolant temp sensor, purchased a new one replaced it and also checked valve clearance which was in spec.
Now after having the tank off the bike starts up fine from cold runs 10 seconds and abruptly cuts off. Will not start after that. I have spark, fuel pump sounds strong, and because it runs at first I know its not timing. Reading some of the post I am leaning towards PCM or connectors, TPS, or clogged fuel injector(which would cause a slower die down starving the bike for fuel which is not what I have). I unplugged the Coolant temp sensor and no change, Any ideas?

What I would do on my bike if this was happening to me, not saying that this will fix it, but you have to start somewhere:

Pull the tank, pull the fuel pump assembly, replace the fuel filter, test the pump, at least make sure it's pumping fuel out the red fitting, check the elec connections, especially at the top of the fuel pump, make sure the plugs have not worn thru..

Pull the injector, and clean the little screen in the injector.

Check the tightness of the coil.

Check the wires that run past the steering head, coming out of the relays, and going into the ECU, all are places that bare wires have been photographed.

Check the voltage coming out of the stator, should be 14.4v when running.

Battery should be 12.8v standing.

Thanks I will rule out those items and see what happens

After lots of testing still having issues. The no idle has turned to a no start issue. I have checked spark at coil, the boot, and the plug. Spark seems pretty strong used a tester to the plug and it jumps a decent gap. Going to try a plug to rule that out. Checked compression at 100 psi without adding any oil to coat the rings. When I spray starting fluid into the intake it still does not start. plug is fouled with gas.

Check intake boot for cracking.

Did you mean the plug is wet before you tried 'starting fluid'?
If so I would (if you have't already) replace the plug with a known good one & retest, if that gets wet by fuel, you may have a leaky injector.
Pull it out & take it to an efi specialist (car guys) that can clean injectors off the vehicle.
They should be able to test the spray pattern/sealing of your injector on the test bench & it shouldn't be costly.

I don't know these model bikes at all, but if you have correctly timed spark, good compression & the fuel pump is making pressure in the line, it is a fuel delivery issue.
Whether that is a leaky injector or a problem with wiring/ecu or whatever you'll have to track it down

Getting a little closer to figuring this thing out. Come to find out my no start issue was a bad spark plug. I thought early on I ruled it out because it had spark arching against the head but shortly after it must have went to a no spark issue. After a 1 mile test ride yesterday the bike bucks and sputters at mid throttle to upper RPM almost like its starving for fuel. Still racking my brain about whats going on. Next test is the intake boot and looking at the Fuel Pump (anyone know how to test the pump) and maybe a clogged injector. Did a test on injector and it is pulsing like it should be just need to pull it and see if it has dirt in it. Thanks for the help from everybody

You can borrow a fuel pressure test kit from an auto store, I did, had to rig up the connections but I got my pump to test at 50psi from the pump and 43psi from the pressure regulator.

Finally after many months of trouble shooting it seems like the 510 is running right. I was so bummed when I figured out the spark plug issue to get it running just to find out it had hiccup problems at mid throttle. I took the pump out and cleaned everything. Removed the fuel injector and cleaned it. I put fresh gas in drained the old out. I messed with all the connectors and it started running correct. I hooked the fuel gage up and I have 45 psi constant so I have no clue what fixed it and quite frankly don't care as long as it runs. Just got back from a torture test and no issues. I did a ton of research on fuel pumps and the apprila Rvx 550 pump will work for $230 online. Just FYI for anyone having pump issues you get the whole module assembly.thanks for everyone's input