Medium-term exists as a phrase, but it mostly refers to public finance. In this sense, it means:
2-10 years, usually used in reference to bonds. When used in technical analysis, usually a few weeks to a few months. Also called intermediate-term.
Intermediate-term, another option, is also primarily associated with finance. However, people who are aware of the adjectives "long-term" and "short-term" will understand that "medium-term" or "intermediate-term" is between the two.
For any of the adjectives, they describe a property of something. The consequences have the property of being long-term. So you don't need a preposition with them. Compare:
The [Noun] is [Adjective]
The cat is black
The consequences are long-term