What is the ruling if one combines the intention to lift major impurity with an unrelated secondary intention, such as cooling down?

Primary text

If a person intending Ghusl (major ritual bath) also intends to cool their body, their impurity is lifted. This is because the cooling effect occurs independently of the ritual intention, so the secondary intention does not invalidate the primary valid intention, similar to intending obedience to God alongside intending to escape an opponent during prayer.