In episode 13 of The Flash season 1, Firestorm, the combined form of Ronnie & Professor Stein, explodes when Caitlin and Barry try to help him. He was never mentioned after that.
Did I miss anything in between?
The following episode, s01e14 "Fallout" shows that Ronnie and Stein survived thanks to the gadget of the week that was added to their chest. The device that was created using the Tachyon device that Wells had tried so hard to con from the other science laboratory.
The episode concludes with Stein and Ronnie, now stable as Firestorm, leaving for another city to meet with someone Stein thinks can help their situation. They come back as plot demands. This wrapped up the Firestorm/Ronnie plot line until the new plot line in Season 2.