Immoderate is the Latin equivalent of 'profusely'. It's an adverb that literally means 'without measure or rule'. The adverb 'profuse' isn't an equivalent. Instead, it means 'in disorder' or 'extravagantly, lavishly'.
latin word profundere (profusus) meaning to pour forth
The root word of "profusely" is "profuse," which comes from the Latin word "profusus," meaning abundant or extravagant.
He thanked her profusely.
I thanked her profusely.
She profusely thanked her friend for the thoughtful gift.
The medical textbook is profusely illustrated.
His leg was profusely bleeding when he cut himself with the knife. Another good sentence would be, his smile was profusely obvious that he was not paying attention to the teacher.
The man was bleeding profusely from his wounds.
three. pro-FUSE-ly.
Profuse (adverb- profusely) in great abundance, bountiful; pouring forth liberally, extravagant.
After running two miles in the heat of the summer sun, Laurel was sweating profusely.
Profane language is not permitted at school.