Not quite.
The P-40 and the P-** should not change places.
If the P-40 and P-** are both running at 95 degrees then they will both perform below book value.
If the P-40 and P-** are both running at 0-32 degrees than they should both perform above book value.
Now the difference might not be identical (both planes might not drop by 3000ft) but the difference of a few hundred feet out of 3000 shouldn't change the relative standings.
LIke have the P-40 out climb the P-** in one case and climb slower in the other case (weather condition.)
Remember that the you are also comparing 3-5 planes. The P-40 and P-** are trying to climb in comparison to the A6M (and bombers?) and both are going to climb worse than the A6M (and bomber at altitude) even though the A6M is also going to climb worse. Likewise on the Russian front you are trying to see how well the P-40 and P-** climb in relation to the Bf 109 as main adversary.
open to correction.
I suspect this may actually have something to do with it. The early P-39s and P-40s were both underpowered and overloaded. Just at the tipping point. P-39 was a bit lighter but they had shorter and smaller wings
It sounds like field-stripping started a bit earlier with P-40s (as early as Java) and overboosting was already being done by Aussie units by the time of Milne Bay (summer 1942). Meanwhile the P-39s were being shipped with those extra guns in the outer wings, which I don't think they stripped those off right away. With the F4F, they were lucky in that the original F4F-3, used up to Midway, was the peppier one (before the folding wings and extra guns).
Early Allied Fighters
F4F-3 has a 38' wing span with a 260' wing area. Loaded weight was
about 7,300 lbs for a 28 lb / sq ft wing loading
P-40E has a 37' wing span with a 236' wing area. Loaded weight was
about 8,000 lbs for a 33 lb / sq ft (171 kg/m2) wing loading
F2A has a 35' wing span and a 206' wing area. Loaded weight was about 6,800 lbs for a 34 lb / sq fit wing loading
P-39D has a 34' wing span and a 213' wing area. Loaded weight was
about 7,800 lbs for a 36 lb / sq ft wing loading (this is with the wing guns)
Early Japanese Fighters
A5M2 has a 36' wing span with a 192' wing area, loaded weight was about 3,500 lbs for a 19 lb / sq ft wing loading
A6M2 has a 39' wing span with a 241' wing area. Loaded weight was about 6,000 lbs for a 21 lb / sq ft wing loading
Ki-27 has a 37' wing span with a 200' wing area. Loaded weight was about 3,500 lbs for a 18 lb / sq ft wing loading
Ki-43 has a 35' wing span with a 230' wing area. Loaded weight was about 5,500 lbs for a 25 lb / sq ft wing loading (plus auto-flaps)
So based on that, the Japanese fighters seem much better suited to Tropical conditions.
A few lbs difference in wing loading between the Allied types may not seem like much but as I said, all the Allied fighter types were right at the tipping point, a difference of ~300 lbs or 150 hp or so seems to have made a huge jump in rate of climb, top speed etc. The Finns also experienced this with their lighter variant of the F2A. I suspect the P-39 units were lagging a bit in modifying their crates, and they already had the shortest wings and highest wing loading of the major US fighter types.
P-39 didn't do quite as badly in the Pacific as their reputation, they did get some victories (a bit over 300 claims). They definitely did better there than in the MTO. But only one (American) Ace, which is pretty telling.
Conversely, not all the P-39 units did so well in Soviet use. There were a couple which got started in the Kuban zone (which is down in the Taman peninsula on the Black Sea, in Southern Russia) in the Summer, and they didn't do so well. I wonder if climatic conditions played a role in that.