One core hotter than the other

Yes, all cores temps vary, normally core 1 has higher temps, first core to work/process data..
You can monitor your temps using Hw monitor, till they don exceed 70 c, you are fine.

It is fine and perfectly normal as one core wil normally do a little more work than another. Worry if it gets 15C-20C hotter. I've got a 7C difference right now with my quad.