Temperature is a physical quantity which can have various numeric values, which can be high or low. But I often read phrases like "cold temperature" and "hot temperature" on the Internet. A quantity can't be hot or cold, so these look odd to me, although I do understand what they mean. But English is not my native language, so my question is: are such phrases grammatically correct?
Temperature can't be hot or cold -- such a construction is grammatically incorrect. As you correctly noted, temperature is measured numerically, so it can be high or low. Weather, on the other hand, can be modified with descriptive adjectives: I hate cold weather. I love hot-weather drinks.
Please keep in mind that the internet is a giant cesspool of unedited copy and grammatical errors. When in doubt, consult a usage book (I recommend Garner's Modern American Usage -- you can find a used copy online), or check to see whether The New Yorker (which has a great copy desk) has used a given phrase. This isn't foolproof -- most blogposts on its site aren't copy-edited, so TNY has published some errors -- but it's useful.
Use Google for such a search, because it shows you how many times the phrase appeared.
Ex.: site:newyorker.com "cold temperature"
PS: Your English is superb.