The Fire Palace is located in the Oho Oasis.
Mario and Luigi enter the Fire Palace, however, Luigi has to form Mario into a Mini-Mario because the hole was small. Mario meets the Fire God. The Fire God tends to get confused whether he forgot Mario is or has not remembered what he is doing. After he disappears, Mario touches the red orb and as a result, his hands heated up, but it fused his hands.
When the Fire God came back, he remembered. He taught Mario bow to master the Firebrand.