I'm not so sure about that, if the memo RCAF linked is accurate, the test showed that the Hurricane couldn't even outclimb a P-40E, it's definitely going to be left in the dust by a Zero.
According to a couple of these guys the Hurricane can dive as fast as anything the Allies had.
The memo doesn't state that the P40E could outclimb the Hurricane. Here's the US Hurricane climb tests:
http://www.wwiiaircraftperformance.org/hurricane/Hurricane_II_Z-2974_Climb.pdf
0-15K ft in 5min. I think the overheating had to do with using a too steep climb AoA.
P40E:
http://www.wwiiaircraftperformance.org/P-40/P-40E_40-405_PHQ-M-19-1320-A.jpg
0-15K in 6.49 minutes.
Even with a 3min wait at 15K ft it could still outclimb the P40E to 20K ft
Terminal dive speed (Vne) says nothing about acceleration into a dive.