There is no question that the AmiLite will get warm using rechargeables. But it also gets warm using primary cells. It's a small light driving a LED hard - heat is part of that bargain.
Since I don't have a themometer to use for testing, this is what I just did. I ran an AmiLite for 10...
You CAN use rechargeables!
I went home list night and tried some rechargeable batteries in my Amilite T3. As has been noted in this thread, neither the protected RCR123's I received with my Peak CPF special or the protected RCR123's I purchased from Lighthound fit. The AmiLite Battery tube is...
To say "All of them" is too easy. All are really nice lights - I just happen to think that the L1P is the best compromise in size, brightness and runtime. And yes, I have all three (1 ea of L0 and L2, three L1P's).