Are you putting glue down carpet in your house? I only ask, because that's not typically how residential carpet is installed. It's usually stretched in over a carpet pad using tack-strip around the perimeter of the rooms. If it's being stretched in, the only adhesive that would come into play would POSSIBLY be the adhesive for the pad if it's over a concrete slab. The pad is often stapled down over wood substrates. In rare situations, they might use an adhesive for the tack strip on a stretch in job, but that's pretty unusual as well.
All of the mills will have the minimum heat requirements just like Daris said. Changing a floor covering material from a cold area to a warm area OR having the temperature fluctuate while you're trying to install it is a significant problem. The material will be stiff and difficult to work with if it's too cold. In addition, while they are working with it, the material will be changing as it warms up. That's why they want the temperature stable for significant periods of time before and after the installation.
I once had a general contractor who had vinyl tile installed in a new construction building in the middle of winter. As soon as the flooring guys finished the install the cheap butt GC turned the heat off and left. It was over concrete, so when they came back in a couple of days later the tile had all released from the floor because it had gotten so cold that the adhesive froze and went dead before it was fully dried. These water-based glues that we use today do not tolerate cold substrates very well and they can "crystalize" and lose bond when they start to approach freezing.
It takes adhesives several days and, in some cases, even weeks to reach its full cure strength. It will get to 90%+ in the first few days, but it can take weeks for it to fully cure. In general most adhesives we use today will take 30-45 days for that last 10% of cure strenght to develop. Lower temps will slow the cure rate down significantly.
Again, I'd be surprised that they are gluing down your carpet, but I guess it's possible. We usually only see glue-down carpet in commercial installations where padding is not being used.
Something else that many don't consider, if it's an on-grade slab, the subfloor temperature will be significantly lower than the ambient conditions above it in cold weather. It's not unusual for the subfloor to be 10-15 degrees colder than the ambient room temperature. This is another reason that many installers will "crank the heat" up above normal because they have to try and raise the temperature of the substrate to a workable temperature. That's also why the VCT failed in my example above. The room was about 40 degrees with the heat shut off, but the slab was about 28 degrees.
I don't think you've got too much to worry about but all the best!
