All DFW rentals are via a shared shuttle bus to the same rental car center, so little difference there. If it were me, I'd probably Priceline or Hotwire and take whatever I get.
I live here and drive a convertible. This time of year, I go topless in the mornings, usually till about 10 or 11; and in the evenings, after about 8pm. In between, I find it too hot, and just put the top up and crank the AC.