Miss in hot weather

My new to me in the summer of 2020, 2007 XK car had displayed a problem in very hot weather (95 -100 F) that’s not unlike fuel vaporization. The car misses under even slight acceleration, and gets worse under heavier acceleration, to the point of stalling. It will however run fine under steady throttle, and giving it a cool off period resumes normal operation. It does not throw a code, and the check engine light does not come on. It’s been through diagnostics at the dealer but without a code they cannot help. They say it’s not fuel vaporization as that relates to fuel pressure which would throw a code. The car had new cat converters last year by the P.O. There is no insulation obviously missing in the engine compartment. I do note that the fuel line from the tank runs up beside the exhaust down pipe on the left side, but it’s in as manufactured condition.

Anybody have any ideas on this?

Just ideas, here goes:
Do you have access to the fuel trims? Does it read a false intake air temperature? Or coolant temperature? Read those values manually when it misfires. Maybe not the right track. But if it thinks it’s way hot above some point it could get too lean? Generally, it might be the MAF. The engine bay can’t be hotter driving on a hot day than when in sudden heavy traffic.

An intake leak ahead of the throttle, after the MAF, when really hot, maybe.
If it misfires it should normally (not specifically the xk) throw a code from the crankshaft sensor and eventually disable cylinders. The cars I know predict when the next impulse should happen and store the deviation. This way the ECU can tell rough running and detect misfires. Why not?

What happens if you disconnect the MAF or lambda, besides a code.

It can’t really be the cats if they are new and I can’t see it being heat related. Also it would run on the other bank and only tighten up at higher speeds. Not on low speed high load. And it wouldn’t die completely. But kick them just for fun, maybe there’s a rattle.

Something with the tank ventilation would probably throw a code as well if it knows what the fuel pressure is. I don’t know if opening the filler cap a little would aid in ruling it out.
That may or may not exclude the fuel pump and fuel filter. Maybe the fuel pump begins to cavitate when the demand is high and the fuel is hot. That should throw a code. Same if it gets weak or the filter is clogged.

Could it be a case of full load enrichment not happening?

Worst case would be a weak solder joint or so that does something when the parts expand.

Sounds like a clean unmolested car regarding the fuel line routing etc. and not that old either.

Thanks David. I live in the Pacific N.W. and high temps like we had a couple of times last summer are really rare so real ability to test the car is limited. My wife is now afraid to go away in the car which is a problem. I had a '97 XJR that developed a very subtle miss, only noticeable in top gear, that occured when the car was warmed up. No codes. Flailed around at this for 2 years till I finally took it to the dealer. The tech there said if you have missing with no codes it’s almost certainly the computer as it’s the only “system” not wired to throw codes. Sure enough they got a used computer from a wrecker and the problem was solved. He suspected soldered joints opening up as the computer warmed up was the cause. An engineer friend, when he buys one of these cars opens the computer and re solders the joints he can get at. So my primary suspect here is the computer, but just swapping it out and hoping it’s the problem won’t ally some fears of travel away from home.
I should add that the two instances of missing - one occurred slow driving through downtown Vancouver BC on a 100 degree day, the second on a stretch of highway that rises over 25 plus miles to 5000 plus feet. It was mid 90’sF, I was on cruise control at 80 mph, with the a/c on.