Heated socks sounds nice. Often I use a basic $30 heating pad at night combined with thick fleece socks to keep them warm. During the day despite the warm fleece socks and thick slippers I get cold feet. Frankly it gets slowly worse as the day goes on. It doesn’t bother me when I’m walking or sitting but when I lie down during the day to relax or take a nap fuck it bothers me. The heating pack isn’t perfect bc the coldest part is the toes especially and the heating pack is below the feet if you put it on top it has no good contact so nothing. The heat does radiate so it does help.
So my feet actually feel cold so it’s not like my senses are off I actually have cold feet like I feel them with my hands and their much colder especially the toes while in your case it seems to be senses that are like misfiring telling you your feet are cold when their temperature isn’t. Have you tried sleeping with a down comforter. Down is a great material and will last a lifetime as a comforter or jacket. Little annoying to maintain and yes expensive but frankly this stuff is an investment. It’s not the kind of material or comforter that you ever need to replace it’s lifetime. You can transfer it to your grandkids it’s that good. A king would probably cost like $200. I got a very thin very high quality queen size white down comforter with norther Canadian geese. Anyways I forgot how they rate down but it had a very high rating and since Costco very good price for it. I spent $40 on a 400 thread count duvet cover for it. Frankly the duvet cover is what adds most of the weight. Down is super light but traps in body heat. So I can have it be below freezing in my room and be cozy under just the comforter.
I fell you this because it’s both incredibly comfortable, with winter ending you could score a deal on down comforters, and without this comforter lying down my cold feet would be much much worse.
They sell these funky looking down socks for like $25 might be worth a try. It’s cheap and Amazon is super easy returns. Frankly I wanna buy them but my dad would kill me but I think next season I’m getting them except what I worry is how hard are they to walk in. I’d it’s just for lying down and I can’t do anything it’s a bit annoying to put on but might be worth it. Also this isn’t the one you’d have to get they have a million I just searched “down socks” OHOHAI Warm Socks - Ultralight Winter Thermal Foot Outdoor Camping Sleeping Bag Tent for Men & Women https://www.amazon.com/dp/B099WKGZY4/ref=cm_sw_r_cp_api_glt_i_193NV4BN6CH4JB876195