I would love to toss it in the oven but the only ovens I have access to are used for cooking food. Plus I could use the puller for other jobs. I just need to know if the supplied part with the puller kit will work with the smallest bearings in the Zilla cases.

Household oven inside my house is what I always use.  If the cases are clean no need to worry about anything.  Goodluck either way.