5w-40 will only be thinner at cold engine temps, so wouldn't affect operating temps; So really a 15w40 will only be thicker in cold temps on startup - which isn't really ideal or going to help you.
It's only the "warm" temp (the 40) thickness which will be thicker at operating temp; so the only place to go would be 5w-50/60, which is a bit pricey as you will never get any benefit from running that high of a grade oil.

I would say stick too what the manufacturer specs.