Ten days at room temperature is about 34 refrigerated days of equivalent exposure. Room temperature is not a number, so take the pharmacopoeial 20–25 °C and its 22.5 °C midpoint: 17.5 kelvin above the 5 °C middle of a 2–8 °C refrigerator. The ten-degree rule of thumb — degradation rate roughly doubling per 10 K — puts that at about 3.4 times the refrigerated rate. It is an order-of-magnitude statement about a rate, not a shelf life, and the top of the 20–25 °C band runs about 1.4 times faster than the bottom of it. At 34 equivalent days a test is more likely to reassure you than to tell you something, which is a legitimate reason to run it and a poor reason to expect a finding. Either way, record the ten days and the temperature now, while you still know them; an excursion you did not write down is an excursion you cannot interpret later.
This is where the anxiety in this hobby is most out of proportion to the chemistry.
That is the argument for shipping lyophilised rather than for shipping colder. A dry powder with low residual moisture is stable at ambient for months; the pathways that matter need water.
Asking a supplier to hold a shipment during a heatwave is reasonable and the better ones agree; the cost is a week and the benefit is a shorter warm exposure for anything in solution.
Arrhenius kinetics predict approximately a doubling of degradation rate per ten-degree rise and are the standard basis for cold-chain design.
Solutions are a different question and deserve the worry the solids get.