Accepted answer
Start by separating chemical degradation from physical degradation, because they fail differently and they are detected differently. Chemical degradation changes the molecule and shows up as new peaks on a chromatogram. Physical degradation aggregates the molecule and often shows up as nothing at all on reverse-phase HPLC, because the aggregate never makes it onto the column.
For the solid state, residual moisture is the dominant variable. A cake at two per cent water is considerably more stable than the same cake at six per cent, because water is both a reactant in hydrolysis and a plasticiser that lowers the glass transition temperature. This is why a desiccant in the outer packaging is not theatre, and why opening a cold vial in a humid room is a genuine error — you condense water onto the cake.
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.
The licensed semaglutide and tirzepatide presentations carry in-use periods of several weeks at room temperature in their labelling, which is the closest thing to real stability data in this space — and it applies to a buffered, surfactant-containing, preservative-containing formulation, not to a reconstituted research vial.
One qualification: none of this addresses sterility. A vial can be chemically pristine and microbiologically compromised, and a chromatogram will not tell you which.
The single highest-value change most people can make is buying a cheap logging thermometer, because it converts an assumption about their storage into a record.