My moms first generation BRG miata has developed a steaming problem. My mother was driving it on the highway and the temperature gauge went to full temp so she wisely pulled over and called me for help. I arrived and filled it up with water and we made it 4/5 of the way home before she pulled over to tell me that it was working fine and i could go to my house. At this point i steam poured out underneath her car and told her to shut it off. After a brief inspection i noticed that the water was not coming out of the overflow but seemed to be coming from somewhere underneath the intake (just a guess i saw no water escaping as the car was off). She said that the water temperature only went up when she stopped to tell me i could stop following her.
Probably causes?

