Overnight Friday, the GFS suggests a cold front to form from the low pressure system, which could track quickly into the southeast with help from the mid-level jet. The cold front is shown to set up in an east-west orientation over the southern Plains and pushing southward into the morning and mid-day on Saturday. The front could bring some small (less than 0.1 inch) amounts of precipitation during the morning due to approaching colder air undercutting the warmer air from Friday. Conditions during the day on Saturday could be windy with some stronger gusts possible.
However, the Euro model suggests the cold front won't approach the region until mid-day Saturday, which will allow temperatures to warm through the morning. The approaching front, coupled with southerly low-level winds, is expected (by the Euro) to cause nearly an inch of precipitation through the afternoon and evening. At the moment, the Euro run is an outlier among the model spread, though I wanted to include it in case the models trended towards this result. This uncertainty in the frontal passage timing isn't lost on the other models though as currently there is a 15°F spread for the high temperature on Saturday. Due to this spread, I'm expecting multiple elements of the forecast to change in the next update.
There is more of a consensus among the models for Sunday, indicating conditions will likely be overcast with a slight chance of precipitation due to southwesterly .low-level winds bringing moisture to central Texas from the Gulf. However, much like Saturday, there is a large spread in the temperatures for the day and I expect the values to change between now and the next update.