Cat's "inside corner" eyelid doesn't look too good

Hi,

I have two indoor only 3 year old kitties (brothers). I live in NYC and when the warm weather arrived, my orange tabby started acting really lethargically, which I chalked off to the warm weather. FYI, when we first moved to NYC last summer, both cats acted the same way because they were unnacustomed to the window unit A/C (we previously lived in places with great central A/C).

Anyway, my kitty's lethargy still seemed a little off to me and when I looked at his eyes this evening, I was scared to see how brown his corner eyelids looked (not quite sure what they're officially called). One part even seems more swollen and dark than the other. I'm going to call the vet first thing in the morning but right now I'm really worried and upset and would like to know what kind of illness he could possibly have. I'm also really worried his illness has been going on for a while and I just haven't noticed (I just finished my first year of law school and was very single-minded during finals). If anyone has any thoughts, please let me know. Thank you in advance for your help.

I am glad you will be going to the vet first thing, but consider an emergency vet right now-- any time you can see that eyelid (called the third eyelid as far as I know) it is bad news unless its a temporary thing while they're sleeping.

Do you have any way to take their temperatures?

I don't know if it has anything to do with the heat, are they seeking out cool spots like tile floors, dark, vents, etc?