Why is there no mention of IR (heat) radar? As far as I know, its impossible to hide a jet engine heat signature. Thermodynamics 101. This is especially true when you are looking up and the thermal background is pretty much black space.
The heat signature of what, the exhaust? That's very low density, so emissions from the exhaust itself will be negligible.
The plane itself will emit black-body radiation, but that is based on the skin temperature, not the temperature of any interior engine parts.
In the meantime, all of this is for passive detection, so at a distance you'd be asking for the detector to pick an at-best-tiny signal out of the entire sky. Moreover, clouds are opaque.
I guess you have flares, but now its an "AI" problem of choosing the right target.
Don't forget the inverse square law of light, by the time the energy reaches a detector on the ground, the signal has weakened considerably.
Skimming wikipedia for infrared stealth gives me "Infrared Search and Track" systems which are plane-mounted, which makes a bit more sense to me -- if you're closer to the targets altitude and velocity you'll get much cleaner data
Generally, it also helps to fly toward the enemy. This is a bit of extra incentive to not wimp out and flee. :-)
The F-35 is a bit of a failure with the heat signature. The tail heats up from the engine exhaust. There are prohibited maneuvers that damage the tail due to heat.
Aircraft don't have to be perfect about heat signatures. They aren't in a cold vacuum, and the enemy isn't flying the James Webb Space Telescope.