Phono preamp hum

Does that unit have an AC filament supply?  If so, I could imagine that there is a leak of AC into the signal that takes time to occur when you start from cold, because something needs to heat up before it leaks. It's important to know that this is a real "hum", meaning 60Hz or 120Hz pure tone.  If not, we will start over.

I have no idea if it has an AC filiment supply.  It has a wall wart power supply.  Once it starts humming, it gradually gets  louder and I have to unplug it to stop.

Have you checked the grounding? Make sure the ground wire is tightly secured. Then try removing the ground wire. Is your linestage plugged into the same outlet as the Bellari? If not, make it so.

Yes, the ground wire is secure.  I have tried grounding it a few different ways with the same result.  Like I said, it sounds fine for about 30 minutes, then the humming gradually becomes louder the longer it plays, or even not playing.

It’s impossible to solve this sort of problem “long distance”, once you’ve eliminated the obvious. You did not answer the other obvious question; is your phono stage wall wart plugged into the same outlet as your linestage and amplifier? If not, try that. If yes, then maybe consult Bellari in Colorado. 

Did you try changing the tube?

It could conceivably be a tube socket problem but unlikely to be the tube itself, although strange things do happen. I would try wiggling the tube gently in its socket or even just tapping it with the eraser end of a pencil to see if that changes the character of the hum. Good idea. 

@lewm  No it isn't.  @Kokomo  Nope, I have given up on it.  I have another unit that works fine.

Your OP is dated 11/15, and on 11/16 you already have replaced the unit. Was this just a quiz?

No quiz.  It has been back in the box for a couple years.  I keep looking at it wondering what's wrong.  Thought maybe I could get some help as I am no tube genius.  Maybe I will give it away and let it drive someone else crazy.

I’m sure it’s an easy fix. But the fixer needs physical access to the unit.

I’ve had a bad tube behave like that in the past…I replaced the tube, and never heard it again.

It's equally possible that by removing and replacing the tube, in your scenario, you improved contact at one or another tube pins, thereby curing hum that had nothing to do with the tube itself.