If the material is in the custody of your customer at the point of break-down (i.e. the material belongs to them, has been delivered to them, and is under their control), then it's the customer's responsibility - provided you informed them of the required storage and handling conditions.
If you manufacture and distribute material to a customer via a logistics partner, it comes down to whether is was your company or your customer that engaged the services of that distributor.
If your QMS has approved a storage/distribution service provider, and the use of that storage/distribution service provider results in a customer complaint, then your QMS must sustain that complaint and initiate an investigation with appropriate responsive actions. Those actions might include a performance review for the storage/distribution service provider or the delisting of that service provider.
Put another way, if I were in the position of the customer and received material manufactured by your company that had been subject to temperature abuse, I wouldn't accept any suggestion of my complaint being classified as 'invalid' - regardless of whether the temperature abuse occurred at the manufacture site or while under the control of the distribution company.