Other possible solutions
I find that humidity more then temperature changes cause this but since winter is usually the dry time of year in areas that get cold maybe you are right that the temperature is causing it. You said that the painting is over a fireplace (not the best location since it will get smoke on it but I have 3 fireplaces and have a painting over each so I am also at fault at hanging paintings in this hash environment as well). I just mention that because the painting will need cleaning over time if a fire if burned in that fireplace a lot.
Try wetting the canvas on the back side then when it is wet, tighten it using the pegs. When the canvas dries it will be as tight as a drum.
Also I do not know how this will be in the long run but I have also applied a coat of acrylic gesso to the back of linen canvas and found that it also helps control this kind of problem. (helps keep moisture from getting in from the back.) If you do this the canvas will sag when the gesso is wet and tighten when it dries.
I would not resort to re-stretching completely unless none of this works. I would have the client take it to a good framing shop and have them do it if it needs to be re-stretched Also a acid free paper backing on the frame may help control moisture from the back.
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