In my personal experience, I've noticed a very strong correlation between amount of heat going into an upgrade vs. the chance of a UV appearing.
NONE of the items I've upgraded at zero heat have ever yielded a UV, and EVERY item I've upgraded at ten heat have yielded a UV.
This has been true for both low-star and high-star items of equal heat levels.
I'm not sure how/if relative UV power factors into this. I think UV power might be related to star level in some way.
Based on what I've personally seen, I'm very certain this relationship exists. However, I only represent a handful of data points, so it could be a fluke.
What are other people's observations about this phenomenon. Try to keep speculation to a minimum.
Did you have a 2 star UV item and THEN started upgrading? Because if so, it transfers by default...
As for me, even though it's not smart, I always got my weapons to level 10 before upgrading (usually because I didn't have the money to outright upgrade) and I NEVER got a UV just because of that.
This includes
Hot Edge ->Searing Edge
Calibur ->Tempered Calibur->Ascended Calibur
Spiral Demo Suit->Fused Demo Suit->Heavy Demo Suit
Wolver Cap->Dusker Cap->Ash Tail Cap
Owlite->Horned Owlite->Wise Owlite