I live in zone 8b, in Central Texas. I would like to plant certain things that require a warmer hardiness zone.

My house has a south-facing brick wall in full sun. I have already planted lemongrass and epazote there (though the epazote probably doesn't need it).

What hardiness zone do you think a plant against that wall would be in?

This is not as straight forward as you are hoping.

Are you on top of a hill? down in a low spot?
What about other nearby structures? Drier vents?

Air flow often has beneficial as well as deleterious impact.

As a general rule of thumb... A south facing wall is going to hold stored heat for a while at night and warm up quicker in the morning... so... I'd plant accordingly...
Maybe you gain a half of a zone... But, I wouldn't plan on growing zone 11 tropical plants... without a glass expansion.
That's where I would put a cold frame (or whatever), preventing over-heating would be a problem.

Also consider western exposure...

My guess, at least one zone- I think I have a one-zone-better bed here.

you still could get frost damage, if you get frost. Some (many?) things would grow back from the roots/bigger stems in case of frost/freeze. The soil won't freeze, or won't freeze as deep, for as long, as other parts of the yard.

A lot of people like to push it, plant for a warmer zone. Even if it is chancey, you may get years of success between some losses. You can try...

Agree, this question doesn't have a simple answer. Once you get to Z8, you don't have the hurdle of frozen ground to overcome, so what is left for zone-pushing is finding plants that can survive above-ground frost and still keep growing the next year. Using the zone ratings doesn't help much with this because those in warmer zones don't really consider herbaceousness as perennialness so if it's not evergreen, so few people use those plants, the info isn't readily available. They panic if there is frost, while it might be just a normal part of winter farther north. It's just up to individuals to experiment.

A discussion about herbaceous tropical perennials here, with the examples I've found so far. Apparently such an arcane subject, I'm about the only one tracking this kind of thing, at least in this particular discussion:
The thread "Tropical herbaceous perennials" in Southeast Gardening forum

Since my gardening started in OH, herbaceous perennials are perfectly normal to me. Preferable, really, so I can clearly see the ground over winter to remove baby trees and add leaves/compost.