After copying the recipe for Hot Titanium Ingot from JEI into my AE system the crafted ingots are not the same as the one in JEI.(They appear separate from the craftable ingots.)

Surprisingly the recipe for Titanium Ingots actually requests the crafted Hot Titanium Ingots, not the ones that are in the recipe. This means the system thinks there is no crafting recipe for Hot Titanium Ingots.

The workaround is to change the Hot Titanium Ingot crafting recipe to produce the actually crafted ingots instead of the ones copied from JEI.

It is still strange to me that two recipes both copied from JEI use different versions of the Hot Titanium Ingot even though JEI only lists one version.

I don't think it's possible to fix issues like that on the modpack developers' side in general. Probably wontfix?

It's definitely annoying when JEI quick-fills a weird NBT item on you, but in the case of hot ingots you should do what dougwebb suggested and automatically route hot ingots into your vaccuum freezer, using processing patterns that assume the ingot is cooled coming back into the network. That way AE doesn't have to deal with the extra step and item types in crafting calculations.

That sort of thing happens with a number of items, due to NBT that gets added to the item as part of the crafting process, which JEI doesn't know about. I assume that's what's happening to the hot ingots.

In any case, you should probably just set up an ME Export Bus to send all of your hot ingots into a cooler automatically, and change your recipe to expect the regular ingot. There's no reason to have two recipes, since there is no other use for the hot ingots. Even better would be to use item conduits to move the hot ingots from the EBF directly to the cooler, to reduce the amount of AE2 calculation lag.