Well, usually we don't need to stress the difference. These are not the words that are often confused. Tea cannot be hungry, after all.
Actually, what I was trying to find out is how exactly should one pronounce them. I'm sure a native speaker (and myself too ) would chuckle if I said "My tea is hungry!" To my ears they sound like almost the same word. But I think from what I know of the alphabet Холодний should be said with a kh sound and голодний with a huh sound.
Холодний should be said with a kh sound and голодний with a huh sound
This is true. Also, note that г is a voiced sound, while х is voiceless.