Hello there, I am a Master Automobile Technician certified by Honda and ASE. I can help you with the problem you are having with your Honda!You could have a malfunctioning Idle Air Control Valve or Vacuum Leak. I would do a quick check for vacuum leaks by spraying silicone spray around the intake manifold. If there is a leak it will suck up the silicone and change your idle. If it does then you have a vacuum leak.
You can also try turning out the idle speed adjustment screw on the throttle body to raise the base idle up some,
When it starts cold and idles 1500rpm, that is normal. This is your fast idle valve which raises the idle while cold to help heat the motor up quickly. Once its hot the Fast Idle Valve steps out and quits bypassing the extra air which lowers your rpm.
Idle spec when hot should be 600-800 rpm
The fact that it stalls, makes me think you have either a vacuum leak or even possibly an egr valve which is hanging open.
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