The next big thing? That's a lot to put on one little grape variety, Peter.
There are several decent and moderately impressive tempranillos from the New World these days. Some have been named already. (And Abacela, for my money, is right now the best.) Parts of California, much of southwest Oregon---those are great places for tempranillo. Texas could
be, if only because there's a hell of a lot of ground to cover there. Plus Texas has some similarities to the Estremadura-like zones of Spain and Portugal.
[The trouble with Texas---I was there through the 70s and 80s and did more than my share of boosterism---is that they had a major false start in the 70's (they were encouraged by the "experts"--who were clueless and guessing---to plant hybrids and crosses, which sadly the public had zero interest in, had to to re-think and re-tool and shift over and got a good part wrong (shifted to vinifera, but often the wrong varieites in the wrong places or in the wrong sytles), and then had to deal with a sudden influx of external money/authority which was much more interested in the "things are bigger here, boy; let's make us some money", losing an awful lot of the artisanal focus just when artisanal was starting to get a good grip on the market.] But yeah, Texas has the potential, for sure.
The thing about tempranillo is that it isn't an aromatic grape, and therefore works best when it is being "enhanced" in some way---through blending, through wood/age regimens, or even "shudder" through excess ripening and hang time and raisination. Which the Californians are perfecty capable of and willing to do, of course; much of what California is these days is mass bulk manipulators, after all, ready to turn on a dime when a dime can be earned.
Short answer? I'd love to see more people playing with tempranillo, so we could get enough of a range to see which directions would be best. And get your hands on an Abacela. You'll enjoy it.