Hey Sasha, our climate is pretty mild here, but it can get to over 115+ here in the summer and down to the teens during the winter. I wear merino wool hiking socks everyday of the year. In very cold weather, I put on a pair of thick wool and loosen the laces on my boots and they do just fine. My feet are always comfortable because I wear the wool. It keeps my feet cool during the summer and warm in the winter.
I think that the reason your feet burn is because of the friction between your wet feet and your shoes. The sock isn't doing anything to protect you and in fact, cotton is holding your sweat next to your feet, causing the friction and burning sensation. I mean, I could be wrong. Been there done that on more than one occassion, but I'm pretty sure I'm right about sweaty feet, cotton socks and hot burning sensations on the feet. You really need to wear a liner sock when hiking. One that will wick the moisture away from your feet. Cover it with a good wool (my choice) sock and your feet will remain cooler in summer and the combination of liner and sock rubbing together instead of foot and boot rubbing together, will keep your feet much more comfortable. Especially on long hikes and backpacking/hunting trips.