Peony take the heat pretty good, but don't know about Tarrant county heat. Also of concern is the number of hours of chilling in Tarrant county. Call your county extension agent and ask. If less than 400 hours the chances are they will grow OK but will probably never set a bloom. Al

Neil Sperry is a good authority on growing peonies in Texas. He reccomends not trying to grow them south of I-20.
There are several varieties that seem to do well here but they need to be planted in full sun. I would check with North Haven Gardens in Dallas to see what they have. I have never seen them at Weston Gardens or Redentas.