The baby was taken to an area hospital where he was pronounced dead.
Middleton first told police that the children were in their car seats but then said in a different statement to law enforcement that there were no car seats in the car when the incident took place, KHOU reported.
Police charged Middleton Friday in the case that happened in May.
According to police records, Middleton told police he left his 6-year-old daughter and 1-year -old son in the car, parked outside a thrift store. He said he left the air conditioner running, a movie playing and gave them water and a snack when he went in to shop for clothes, The AP reported.
Middleton turned himself in to police on Monday, KHOU reported.