OK, It maybe that your putting too much pressure on the drill, and actually "melting" the plastic housing on it!
On my Dewalt, the silly "cowl" started to peel off...(I bought one of those "family packs" of tools with the el-cheapo batteries I found out and I will "NEVER" buy anything battery operated from DeWalt again!).
You probably got it too hot, and you started to melt plastic... Just use it in a regular fashion and it should be ok...(I would use it in very "light" drilling, and not drill so long with it, as its heating up on you, and I dont think the brushes have anything to do with it, lets face it, DeWalt battery operated tools SUCK!-->I love thier "corded power tools", but, they dropped the ball on the battery operated ones...).
Get rid of it and get another drill...
I recommend (and a lot of people would be shocked), but, a Sears "industrial" battery operated drill ! I have used my 14.4 volt drill for over 10 years now! And the Battery has lasted up and still holds a charge!
(The reason I wanted that "combo pack" was because of the trim saw for DeWalt).
Or any Industrial brand drill is obviously better than any DeWalt battery operated tools-->Do I get the message across, I dont like DeWalt tools yet?? :)
I wish you well...