The brainstem is just where that diagram says it it: behind and a little below the ear. It controls the critical to life functions --breathing, pulse. If it remains intact, you will not die, just become a vegetable.
Aiming at the temple, as you can see, means you are aiming nowhere near the brainstem. Can you die from a temple gunshot? Yes, if you use a large enough caliber gun that the hydrostatic shock causes collateral damage that impinges on the brainstem. But it's a "bank shot": indirect, and reliant entirely on the shockwave from the bullet doing enough damage to destroy a piece of the brain that is well outside the direct path of the bullet.
A friend of mine attempted to CTB with a temple gunshot. He blew his eyes out of his face and turned himself into a vegetable, but didn't die. He ended up on a life support machine until his family did him the kindness of turning off the machines.
As @thrw_a_way1221221 recommends, have a look at the guns megathread he links to. It should give you adequate technical info for the method.