sorry should have made it clear not talking the point of the variants of x processor vs x processor for the battery solution I'm talking x processor vs x processor for the heating one (even though its secondary benefit would be reduced power consumption even if its not vastly one) and as far as the liquid cooling I didn't expect it to be a solution on its either its more of these things in combination should meant that a Atom processor should not be written if you wanted to use one to power a windows phone as we have seen that an X7 can be used in something as small as a 8in tablet (Predator 8), which is marketed as a gaming android device, and that a Atom processor from 2014 can work in a phone (ZenFone 2) so lets try to meet both half way instead of the X7 which most defiantly would burn hotter than a X5 and would also out perform the 2014 Z3580. As for battery solution we just gotta swallow the pill the phone will have to be a bit heavier and thicker than the current super slim and light phones if you want comparable battery life, and liquid cooling can help aid with keeping the heat down by helping out when the processor gets to hot even if its minimal as the true benefit would be to help with throttling. That is if it works the way it does in the Lumia 950xl which used a 810 which is known for its high throttling and being hot to the touch which plagued it originally from being used in many phones.
More or less this kind of device with its "Challenges" has been partly created before its just that you have to look at how did each part of it fair what worked, what didn't, what can be improved and what was comprised and then in the end figure out if you put those parts together is it with its high and lows is it something someone wants, are they aware of everything that encompasses this kind of device.
These should be the questions to ask
Do people want windows on a phone ?
What the experience would be like to have Windows on a Phone ?
What is needed to run Windows on a Phone ?
What is Wanted to run Windows on a Phone ?
What you can't have on Windows on a Phone ?
What to expect with the expect now that you know what works what doesn't, and the compromises for Windows on a Phone ?
Do people want the experience of Windows that you have the ability offer ?
As a recap is liquid cooling proven to be effective in a phone yes Lumia 950 XL with snapdragon 810, can atom work in a phone besides it being the reason for its inception yes based on the Asus ZenFone 2 which used a quad core variant created in 2014, can it perform is the harder one while the smallest device with the highest variant of the Atom Chip (X7) was in a 8in device so when you make this kind of device smaller it should face decreased battery life, have poorer heat dissipation, and by extension have more issues when it comes to throttling to combat use a lower end variant (X5, X3), liquid cooling, slightly thicker device leads to the ability to squeeze in a bigger battery.
Oh and for the difference between i3 and i5 power consumption in my older Surface pro 3 i5 128 and the i3 Variant my girlfriend owned her device did indeed have a slightly longer battery life when we did our out boxing and battery test as I at the time was more interested in it lasting me longer through my typical school day. Don't remember how much but I think it was around 20 or so minutes longer.