Mojito Mint in Polytunnels

We are interested in growing the mojito mint in the UK, but are concerned about ambient temperatures. We plan to grow in a polytunnel enviroment but wish to keep leaf growth throughout the year. What air temperatures would be required and root temperatures? Would keeping the roots above 0 degrees sufficient to maintain leaf growth? Is humidity a factor to be concerned about?

If you are successful in getting other mints such as spearmint and peppermint to grow in these conditions in polytunnels then you should have success with mojito mint because there really is not much difference in their cultivation requirements. However, I would be skeptical that any mint would produce much when grown in temperatures under 10 degrees Celsius. At low temperatures above freezing the plants will enter a dormant state and anything you harvest will not be replaced by new growth. If however overnight low temperatures are followed by warmer daytime temperatures over 10 degrees then you will get replacement growth and you will be able to get some repeat harvests through the cooler season.
Humidity is not a major concern, but if you have excessive condensation drip on the leaves you will encounter problems with mildew. You will need to manage condensation by ventilating the polytunnels.