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.
The temperature dependence is roughly Arrhenius over the range that matters, which in practice means every ten degrees of increase roughly doubles to triples the rate. Ten days at thirty degrees is therefore comparable to something on the order of a month or two at four degrees — bad, but not the catastrophe it feels like when you open a warm parcel.
On re-freezing something that thawed in transit: if it arrived as a lyophilised solid that warmed but never got wet, re-freezing costs you nothing except the thermal cycle. If it arrived as a solution that thawed, re-freezing adds a second transition and therefore a second dose of ice-front shear. The asymmetry is worth internalising.
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.
If the material arrived warm and it was lyophilised, test it and proceed on the result. If it arrived warm and it was in solution, the result is more likely to be interesting than reassuring.