I've been finishing my basement for the past year and a half. I decided to go with 1" rigid foam board glued to the concrete block, 2" of rigid foam on the rim joist, and a layer of Roxul in a 2x4 stud wall. Since I have a waste pipe running across the entire back wall, I decided to build the 2x4 wall a foot off the foundation to neatly hide the waste pipe. I also also decided to relocate the hot and cold copper pipes behind this wall. Although I knew this dead space between the framed wall and the foundation would not be as warm as the rest of the heated living space, I figured it would not come anywhere near freezing temps.

Well, nothing has happened yet, but the sub-zero temps we've been experiencing have me a little concerned about the copper pipes.

After noticing a much colder floor just above that dead space, I took some temperature readings with an infrared gun. With an outside temperature of about 0*F, the area around the copper pipes was about 48* and the rest of the basement was 64*. Something else to know is that the wall has not been sheetrocked yet and I have three small sections of the wall without insulation because that's where the access panels will go.

Once the sheetrock goes up and the plastic access panels are in place, do I need to worry about the temps dropping low enough to affect the copper pipes?

Even if the pipes are safe, I still need to do something about the cold floor right above the dead space... especially since the tiled bathroom floor was really cold near the toilet and the wife was not happy.

As of right now, I have the Roxul installed in the 2x4 wall and in the joist space right above it (see attached picture). I was thinking of taking the Roxul in the joist space and pushing it back against the rim joist. Then, I would install another piece of Roxul perpendicular to the 2x4 wall (see attached drawing). This would hopefully allow warm basement air to reach the copper pipes, but not mix with any colder air in the dead space.

Do you think moving the insulation as I described will make a difference?

Thanks,
Logan

I'm a former DIYer. I did a lot of research for my parents' house some years ago, but they died and the house was sold.
The subject of foundation insulation, and basement finishing, is constantly improving.
Unfortunately, except for This Old House and some contractors who take the time to study the latest, many problems still result.

The first is rigid foam glued against the foundation - both outside and inside are now deemed to be worse than useless. Outside, bugs crawl in and make so many tunnels that in a few years it looks like wormwood. Inside, because of moisture getting through, increasingly over 40 years of curing resulting in more and more tiny bubbles, the seepage weeps down to the bottom, where more bugs have a field day, especially termites and carpenter ants and pill bugs (pill bugs being harmless), and if there's enough weeping, it rots the stud wall and gets out into the finished space. There is NO good interior water block paint. The water pressure is too great.
You did say BLOCK. I don't know the story on block, but like any foundation, eventually it needs repairs. I investigated poured concrete. But I would never finish a basement unless most of the foundation is accessible.
The new approach is 2' x 8' foam flat on the ground buried 2' down (with other materials on the wall itself). Inside, a wall is built back from the foundation (as you did) and insulated with fiber or foam or both inside that wall, not against the concrete. The bottom plate is PT. TOH puts spacer studs out from the concrete every 4' feet. I think they prefer metal studs all around the basement.

For your bathroom, I would put a few square feet of electric heat flooring against the subfloor and while you are at it, wrap some electric around the water pipes. It's nice to not have to sit there running ice cold water in the bathroom. I don't know if it would freeze. I'm in CT and have had the same temps as you. I was planning to go away and turn my thermostat down to 45. But none of my pipes are near the basement walls, nor near outside walls in the living spaces. What if you wanted to go away?

I would ask a basements only contractor to look at your work. He might want some work and say anything, of course, so it might be worth it to pay for 30 minutes of his time + travel.