Battery question

so I'm perusing the goodies in the RCM storefront...and I see a 3200 25c 4S.

We have a race coming up on 23AUG...and I'm looking to get more batteries for the three classes I'm entering. I'm wondering about this 4S...will it help keep the motor cooler? Will it have less strain on the ESC?

I've been trying to keep up with the logic of higher voltage and less amps being the key to more efficiency...but truth be told I'm having a little trouble grasping the concept.

So....the question I'm asking is basically this:

in a triad of mains (2 7min quals and one 7-10min Main), will it be more effective (better speed and power, lower motor temps) to run a 4S with lower mAh or will I be better off with running my TP 3S 40/80c 5000mAh?

I'm thinking the extra voltage of the 4S would be able to make up for the lower amps the 3200mAh pack has versus the higher amperage of the higher capacity 5000mAh 3S pack.

And then you have the weight benefits of running a lower mAh pack.

and what about runtime? would I be able to last at least the Main with that 3200 mAh pack?

please advise.