No, lots of personal feelings, states and conditions are conveyed using avoir instead of être. I'm sure you've come across some already.
J'ai faim / Tu as faim ~ Literally I have hunger / you have hunger, but in English we say I am hungry / you are hungry.
Same for goes for thirst (soif).
Even when stating our age we use avoir. J'ai vingt ans. Literally I have twenty years, but in English we would say I am twenty, or I am twenty years old.
"Tu as froid/chaud" describes somebody feeling cold/hot (it is literally to say: you HAVE cold/hot).
"Tu es froid" implies more about a person's personality (more like saying: you are a cold person, a general term like they are not very emotional or loving.
Beware of using "tu es chaud" as this has sexual connotations, a bit like saying "you are horny". I hope this helps a bit :)
If there is no gender specified the adjective is always assumed as masculine. If you were referring to a female then use appropriate version.
I guess there is simply an exception to use "as" if used to describe one's body temperature? Are there other similar exceptions?