Matthew 3:11 I baptize you with water for repentance, but he who is coming after me is mightier than I, whose sandals I am not worthy to carry. He will baptize you with the Holy Spirit and fire.
See also Luke 3:16
This is the inspiration for the hat. Believers in Jesus Christ are indwelled with the Holy Spirit. As believers, the Spirit burns in our innermost being of soul and spirit. Fire is the symbol that identifies us with Jesus Christ. He does the work. Fire will purify, separate, and cleanse our actions and thoughts.
As an aside, we think flames are ultra-cool.