Water Line freeze protection

Hello to all, I'm building a bathroom and pulling water from the main house to a barn loft where there will be heated, insulated space in the new bathroom. The problem is I must run the supply thru an unheated attic (I'm in Vermont), where the temps are identical to outside. There will be around 15 ft of run that will be vulnerable and I'm wondering what the best strategy would be for keeping the pipe from freezing. I'm planning 3/4 pex, which will be split into hot and cold once it arrives to the bathroom area. So far, we've thought of creating a chase with 2" foil faced foam that goes thru the uninsulated space, but I still think it will need to be heated inside somehow. The run passes thru a utility room with a forced hot air furnace and I was considering tapping from the plenum with a very small duct (2"?) and feeding some hot air into the chase whenever the heat kicks on. The other idea is heat tape, but how permanent and reliable is heat tape? Another thought is to just open the end of the chase to the heated utility room and let the warm air move thru the chase without the pressure of tapping from the plenum One problem with this may be that the pipe runs downward away from the heated utility room thru the unheated attic space, so convection won't be on my side. . Any other ideas? What have others done that has worked? Thanks, CT

I think you chase idea is very do able

I'm with frodo
Heat tape will crack and disintegrate after a few years exposing the wires inside thus creating a fire hazard.

heat tape is a very bad idea...crap outta be outlawed