SOPS
I can't speak about modern aircraft but the older ones that I have worked on did have nose wheel brakes. These were referred to as "spin brakes" and were friction pads fixed in the nose wheel bay. When the undercarriage was retracted the nose wheels contacted the friction pads and were "braked" to a stop. This prevented "nose wheel rumble" when the nose gear is retracted. The main gear is braked by an autobrake for the same reason. I have never heard of nose wheel spin brakes catching fire though!!
Hope this is of some help.
CC