This is a rate equation with respect to time, so you need to work temperatures at various points in time, not just at some arbitrary starting point. Two laws of thermodynamics must be adhered to:
1. heat flows along a gradient, from hotter to cooler
2. total heat does not change, it goes from one place to another, but it is never destroyed
So when you're riding you've got two things to consider. The heat-source is your body and you'll generate a certain amount of heat, BTUs per hour, based upon how much you're exercising. This heat is higher than the outside ambient temperatures so some of it is radiated away. A more significant amount goes into heating up sweat and evaporating it, which absorbs away 540kcal/mole of sweat. A significant factor in radiating and evaporating heat away is surface-area.
As for heat in the helmet, that's a hard one to work with. You've got limited amounts of exposed surface area to radiate and evaporate away heat. I suspect the fastest way to cool your brain would be to have as much surface-area as possible, no helmet at all. we can use that as a 100% control figure. I'm not how to measure how much a helmet blocks at rest at a stoplight. With that figure, we can then compare cooling rates with and without something between your head and the helmet.
The thing is, increasing one cooling method may be counter-productive to the other. using something to faciliate radiating heat away may slow down evaporative cooling and vice-versa... I supposed the best method would be to have something between your head and the helmet that's continually at a lower-temperature than your head AND the outside air... which would require active refridgeration...