I always wear my radio in my strap under my coat. Any time a handie talkie, whether it's the speaker mic, the cord, or the radio itself is exposed outside of the protection of the coat, it can potentially melt. At least the radios my department uses are not made to withstand heat. They're basically everyday radios that many construction companies use. That being said, wearing your radio and strap under the coat works the best I've found. Some guys like it better having their radio in their outside coat pocket because they complain they can't reach the mic under the coat. That's all well and good, but the antenna, speaker mic, and in some cases the top part of the radio itself is outside of the pocket can be exposed to the elements. But that's still better than guys who put the radio in the outside coat pocket and wrap the speaker mic cord around the back of their neck, letting the mic dangle down the opposite shoulder. By doing this, the cord is exposed completely and the firefighter can't see it behind their neck, so they may be screaming a mayday message into a mic that's completely dis-attached from the radio itself without them knowing about it. I personally like having my radio on a strap under my coat, but it all depends on personal preference, just so long as the radio is protected.
I've also noticed that the FDNY wear their straps on their left side. I never really thought about it, but does anyone know if there's a reason behind it, or is it just a coincidence?