hcxt2001
it could be a multiple issues and simple enough...
that rubber cap, needs to be vacuum tight and will cause stalling..... get that replaced.
Does your bike have an updated tune? ..... that has caused problems in the past..... they will have a tendancy to die off at idle.... i.e... when pulling up to a stop sign once warm.
I do not believe it is your engine crank sensor...... 99% of the time when it goes.... bike will not start at all...... But I do know of one that when it got hot, he'd pour something cool on it, and it would run another 20 miles....
TPS sensor could easily be sticking...... and this makes sense if it is governed by the engine being warm or not... Take it off and clean it up... while there...... check out the IAC. WARNING, the center of that IAC will tend to shoot across the shop floor....... lost for ever..... handle with care....
Check all of your intake gaskets. The throttle body gasket is getting rare, (silicon will work fine), but I've pulled one of those off, and it was folded over. Intake gaskets at the heads could also be a problem.
once you've done all of that, and still have a problem, we can do some trouble shooting.
Bruce