A couple things:
A tube that is properly encased in a tire/rim is under very little stress (like almost zero).
Either the tube was improperly installed or hole was suddenly created in the tire/rim.
If the later did not occur, then revisit your installation procedure. The tube may not have been properly seated at the valve, causing the tube to fold under itself and stretch at that point. The tube must be installed with adequate pressure for it to have shape, and you must ensure that the sits straight (not twisted or folded), and the valve area must be pressed against the rim before inflating.
The problem with the Michelin latex inner tubes however is that they're just too long making correct installation nigh impossible.
One possible solution to that is to opt for the smaller 18/20 model if you can find it.
Yet an other option is to cut the inner tube, remove whatever amount of slack there is and glue it back together. It's not that hard to do.
Of course the easiest way of all is to avoid those green latex inner tubes (which really are inferior latex tubes to begin with) and get yourself the real thing as used in top quality tubular tyres namely Vredestein latex inner tubes. They're way lighter too.
@szculdo: From looking at the pic of your inner tube I can assure you that it was neither heat, nor excessive braking that made it blow up.