It helps to be literal here: freeze-thaw damage happens at the moving ice front, not at the storage temperature. Once the sample is frozen solid and cold, very little is happening. The damage is done during freezing and thawing, which is why the number of cycles matters and the duration of the hold mostly does not.
Freeze-concentration is the mechanism people miss. As ice forms, everything that is not water is excluded into a shrinking unfrozen fraction, so the local concentration of peptide, buffer salts and preservative rises sharply. If the buffer components crystallise at different rates, local pH can shift by more than a unit. That is why a phosphate-buffered solution can behave badly on freezing while an unbuffered one is fine.
On the detail: practical thermal arithmetic for a shipment: a single 250 g phase-change pack in a thin-walled polystyrene box holds sub-ten-degrees for roughly 24 to 48 hours in a 25 °C ambient, and considerably less at 35 °C. Any lane taking eight to fourteen days is therefore not temperature-controlled for most of its duration regardless of what was in the box, which is the argument for shipping the material lyophilised.
The Arrhenius relationship underpinning accelerated stability testing is the basis of ICH Q1A, which is why accelerated studies at 40 °C and 75 per cent relative humidity are used to predict shelf life at 25 °C. The same relationship lets you reason about a warm transit lane, with the same caveats about extrapolation.
One qualification: none of this addresses sterility. A vial can be chemically pristine and microbiologically compromised, and a chromatogram will not tell you which.
Minimise transitions rather than minimising temperature. One freeze and one thaw is fine; five is a different question.