No I don't get a burning smell..still can't figure out where the beep is from.Not too sure if this will help but i had a constant beep on my 98 F3. This turned out to be the regulator/rectifier. It was boiling the battery. If you take it for a long run do you get a burning smell of plastic from where the battery is?
I did blow my regulator rectifier sometime back and replaced it with an oem one.The battery is new too..As for the overhaeting,the bike runs in the normal temp.range..Did'nt find anything in the manual regarding trouble shooting for this constant beep..Have you had any issues with your battery or issues with the bike overheating?