How you ever wondered about how to use rather and how to express this case in German?
In general we use this grammar in order to correct a statement, indicating that the second statement is more accurate than the first.
This happens quite often, let's assume we saying x and in the same time you recognise yourself, that y is more accurate for describing the situation.
E.g. It's not cool today, rather, it's almost cold.
(When writing this, it's almost end of october, and it sometimes happens, that's not only chilly, at late hours it's getting already quite cold.)
In German we use the grammar "nicht ..., sondern ...".
Es ist heute nicht kühl, sondern kalt.
A bit more going with the flow, we would say:
Es ist heute nicht etwa kühl, sondern eher kalt.
In Japanese we would use 「というより」.
今日は涼しいというより、寒いくらいだ。