From Sean Bellafiore:
Another week of showers and thunderstorms is ahead for Central Texas as an upper-level disturbance moves in and stays overhead for a few days. Morning rain today will continue to exit from west to east and by the late morning hours, much of Central Texas should dry out. Although there's a low chance of rain this afternoon, much of Central Texas remains dry with high temperatures in the middle and upper 80s.
An isolated thunderstorm or two is possible west of I-35 overnight tonight, however rain chances will remain low. Clouds return back to our skies with morning temperatures in the upper 60s and low 70s. The upper-level disturbance and associated cold front begin to move into Texas Tuesday morning, but showers and thunderstorms should hold off until the late part of the day. There's a very low chance of strong thunderstorms late Tuesday afternoon into the evening. High temperatures only reach the lower and middle 80s due to mostly cloudy skies.
Rain should become a bit more widespread in nature Tuesday night as a cold front approaches the area. The front will start to stall out Wednesday morning, keeping rain chances high for the middle of the week. Off and on heavy rain will continue for much of the day Wednesday, Thursday, and Friday, leading to a flooding concern. Due to cloud cover, the severe weather risk will remain low, much lower than normal for early June. Although the heaviest rain will be Wednesday through Friday, more rain is possible Saturday and Sunday. 2-5" of rain with locally higher amounts is possible across Central Texas through Sunday.