In a 38L it takes around 3 minutes for the engines to cool down after you kill ‘em.
I suppose if one was inclined, you could perform a few engine temp tests and how they correlate to WEP.
I don’t see crates sitting on the rearm pad waiting for their engines to cool down.
When I get home from work tonight I will test the nonesense I have just posted. What’s the worse that can happen 

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Not sure what you mean by "temp tests and how they correlate to WEP"? They are 100% correlated. The temp meter is the WEP indicator. When you reach a certain temp you are out of wep. In reality planes may have had a methanol, or Nitros Oxide gauge indicating when they ran out. IIRC HTC rolls them all into the temp gauge. when the gauge drops you get your WEP back.
Apparently there is a total time limit for WEP on planes with WEP. We don't know why. If it is temperature based, it makes no sense to have a total WEP limit. for planes with ADI or Nitros it doesn't make sense that it's not replenished with fuel and ammo. So what we are all wondering is why it is set up that way.
The OP wanted it changed so the overall WEP timer is reset on re-arm. I am for the overall WEP timer being reset on re-arm, but not to the cool down timer to reset. so if it takes 10 minutes for a 109 to get 100% of WEP back, when you take off from a rearm, you still have to wait 9min, 30 sec.
So I give the OP a +1
...because it makes sense.