The Fireproof Batsuit was built to withstand any fires and other forms of extreme heat so Batman would have protection against such dangers. The suit was instrumental in Batman's first defeat of Firefly.
After a few encounters with the new villain, Firefly, and Batgirl had been injured in a fire caused by a booby trap in his workshop, Batman donned the fireproof suit to prevent Firefly's weapons from hurting him and to navigate properly in large fires caused by them.
Many years later, Batman built a new Batsuit to compensate for his advancing age. Among many other technological advancements over the older models, this suit was made strongly resistant. This allowed Terry McGinnis (the new Batman) to walk through fire when needed. It is possible some of this resistance to heat, electricity, and radiation was derived from the same methods used for this suit as many other features of that suit were likely derived from other equipment Batman had used or encountered.