Generally no. The last time I wore a hat was for a manufacturing course's lab. It was the welding portion, and everyone had to wear a hat of some sort (though nothing polyester). It's bad when sparks land in your hair and start a fire therein.
Cutting through steel with a torch - damn it's crazy, sparks and little blobs of metal flying everywhere. As I remember it, the torch heats up the metal to the point where it's just about melting. Then to "cut" it, a trigger is pressed, which blasts oxygen down into the metal, blasting away the liquid stuff, leaving a cut behind.
If I need to do yardwork, I will also wear a hat then - a white hat, saturated with insect repellent. My hair really heats up in the bright sunlight, and it starts to heat up the rest of me too much. White hat on head helps considerably with that.
Outside of those two occasions, I haven't worn a baseball cap in at least 10 years.