mini Tesla PN2222A transistor getting hot
See Understanding the slayer exciter circuit base voltage for a full explanation, but you are basically abusing the transistor in two ways:


By leaving out the diode, you're forcing the B-E junction into reverse breakdown whenever the base tries to go negative.
The 2222 is a small transistor, only good for a few hundred milliwatts of dissipation. It's hard to say what this circuit needs, but it could be considerably more. And issue #1 is only making matters worse.