After we get past the near daily chance for thunderstorms (some severe), the rain should taper off and the heat will get turned up.
Forecast models have been advertising an upper-level high developing over the southern US. This high will allow for compression in the atmosphere causing temperatures to rise. Take a look at the 12z GMT (7am CT) weather service Global Forecast model's depiction of temperatures over the next week.
The red line indicates the surface temperature. The green line indicates the dew point temperature. The green columns are accumulated rainfall amounts.
Note the temperatures climbing in to the low 90's by mid-week. I think the models may be slightly underestimating the heat coming in. I wouldn't be surprised to see some mid 90°'s (94°) by Thursday or Friday.
When you combine the surface temperature with the dew point, the heat index will be in the upper 90°'s.
I'm really not a fan of these temperatures...