A F4U-4, Spitfire Mk XIV, La-7 or Bf109K-4 will all beat one if it tries to play.
How does its high speed handling compare to other speed kings?
The F4U-4 does have a better high speed handling and does outturn you by a huge margin. You really have to be very very careful around that bird as a Temp driver. You have better sustained climb rate, but the F4U-4s zoom climb capability may deny you that advantage. You are considerably faster (~30mph) at around 5-7k, but really using this speed advantage may lead to what many would call "weak flying". Above ~18k, the F4U-4 pwns you in almost every way. But even below I wouldn't recommend any close-quarter dogfight, you most probably will get slaughtered very quick.
Against Spit XIV:
You are faster up to about 8k, slower from 8-14k, faster again from 14-21k. Try to memorize that stuff. The 14 is one of the few planes capable of outaccelerating the Tempest, and climbs much better at any altitude. But the 14 has two distinct disadvantages high speed handling sucks, in a very fast dive it's roll rate is pretty much nil, use that advantage against the Spit. Surprising ly to most players, the Spit 14's tunring radius is only slightly smaller... many occasional Spit 14 pilot do actually lose a turning contest with a Tempest.
And, last but not least, the Tempest is a much more stable gun platform. The wobbling nose of the Spit may save your Tempest from time to time.

La-7:
Outturns you,has about the same climb rate, acceleration also about on par. You are faster, but only about 10mph at most altitudes which isn't that much. But there's special altitude I want to call your attention on: from abut 6 to 8.5k your Tempest is faster on MIL than a La-7 on WEP. If you like insulting PMs and derogatory comments on 200, you may drag the greedy LA until it's fuel runs out. But of course that's really weak. Still, I do it from time to time

109K-4:
Against the LA you tried to keep the fight away from deck, against the K-4, go LOW.
Your high speed dive is much better then the 109's which suffers from control stiffness above ~450mph. On the deck, you are not only faster (an advantage that lasts up to ~8k), but your climb rate is also on par (but only up to ~1.5k). Your turn radius with and without flaps is actually smaller than a 109 (Again this is often not known to many players], but the advantage isn't big enough to call it a decisive edge. It basically boils down to pilot skill.