I have a 1998 Toyota Avalon that runs fine when cold. After it is thoroughly warmed up, it occasionally has a misfire. The misfire clears if I aggressively rev the engine a few times, or if I accelerate hard enough to make it shift down as if to pass another car (which my wife hates but I enjoy) When it is doing this, I have examined the exhaust, and it makes black smoke.
Talk about maintenance - what is or is not up to date?
Check your fuel pressure regulator.
You need to get the car scanned for codes. AutoZone, etc. will do this for you free.
It very well could be a leaking fuel pressure regulator. It is not as noticeable when the engine is cold because a cold engine requires more fuel to run properly than a warm one.
When the engine is warm the engine is trying to load up as it’s called and the aggressive revving or hard acceleration is simply the engine clearing out that excess fuel.