Sweat: the sweat in the eyes is the big factor.
Sunburn: white color helmet liner that doesn't interfere with suntan lotion, not red color or black color.
Cooling: front, top, side vents are just part of the solution. Its how the air passes through those vents and out to the back of the helmet.
Variable solution: before you go out and buy a skull cap or liner, try a kitchen type paper towel that's known for its absorbance. I use Viva by Kimberly Clark.
https://vivatowels.com/en-us/viva-mu...e-cloth-towels
Why variable solution? Because that towel comes in perforation of three sheets, smaller sheets to fit the inside of the helmet and padded to where it counts, up front where the sweat pours down to the forehead and eyes. The other "variable"? Very absorbent because it was designed for kitchen use.
On very humid days, you may store extra Viva towels in your back jersey pocket. That way you may switch out while the used towel dries out. And yes, they do dry out very well.
On not so humid days, I find that these towels can be re-used several times.