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I just recelled a Quantum Turbo battery.
I've charged it, then discharged it using a Quantum T5d-R fired by radio from a camera body set to shoot on a 4s interval.
Set to Ultra Fast, the battery provided 156 full power flashes... 10 minutes.
The T5d-R flash tube was hot at the end of this, but nothing was melted and nothing cut out.
If you feel that you might need to use any sort of burst mode or use full power outputs as fast as your flash can recycle then you would be advised to buy a flash that can cope with this rather than shut down when you most likely will least want it to happen.
You will get more successive shots from a Speedlite at night in low temperatures than you will at midday in the dessert, so it would depend on a number of factors before you reach your burn out point.