US military issue ammunition is required to fall within a Standardized Agreement (STANAG) weight/pressure/velocity range for compatibility among NATO allies.
That said...
U.S. Cartridge, 9mm Ball, NATO, M882 (DODAC A364)
Bullet Weight: 112 Grains
Velocity: 1263 ps (+/- 5 fps), 15 ft. from muzzle
Case Mouth Pressure: 31,175 psi (avg), 36,250 psi (max)
Intended for anti-personnel use in Pistol, M9
Also approved for the following non-standard weapons:
Pistol:
HK P7 Series
Walther P38
FN P35 (Browning High Power)
SMG:
HK MP5/MP5SD
Beretta M12
IMI UZI
Sten MK II
Sterling 12A3
FFV M45/45B (Carl Gustav)
Madsen M50
CZ M23
As you can see, this performance was designed to function in both WWII era and more modern pistols/SMGs.
A few countries have designed purpose built hot SMG 9mm ammo (e.g., Finland). It is rarely encountered in military circles but may occasionally pop up as military surplus.
The US also has (had?) a type-designated 9mm SMG round:
Cartridge 9mm, Ball (DODAC A360)
Bullet Weight: 115 Grains
Velocity: 1125 fps (+/- 90 fps), 15 ft. from muzzle
Mid Case Pressure*: 38,500 psi (avg), 43,000 psi (max)
*Note: Mid case pressures normally run 8000 to 10,000 psi higher than case mouth pressure.
This round was designed to operate a 9mm modified M3 SMG (Greasegun) which was never put into general issue. The round is specifically prohibited for use in the M9 pistol.
Over almost 30 years of extensive military small arms firing (including all the weapons mentioned), I've only used SMG-only 9mm on one or two occassions. Normally, we just use M882 for both pistols and SMGs.
My experience w/ European commercial 9mm (such as the Fiocchi mentioned by Harold Mayo) is that it is loaded slightly hotter than US commercial counterparts. But this holds true for their other pistol calibers as well. Fiocchi .357 is noticeably snappier than most American produced rounds.
European sport shooters are used to generally higher velocities from their manufacturers...performance many of us can remember from Remington and Winchester loads of yesteryear.
I think Americans have just gotten used to lawyer-induced ammo which mitigates corporate liability for the manufacturers. Kinda like getting Americans hooked on dry-roasted coarse ground coffee (a coffee industry cost savings) vs. the rich fine ground that everyone else in the world drinks.
I've been firing NATO 9mm for years in other countries and out of most service pistols. I never once walked away from firing thinking, "Wow...hot ammo". I've fired significantly hotter commercial ammo (including 2000 fps THV) thru military weapons.
In answer to your original question, NATO 9mm is not hot +P. More like warm.
Hope this helps...