Hypothetical: is this probable cause for a warrant?

Assume the following facts:

A criminal suspect is arrested, with ample probable cause. An inventory search post-arrest yields a receipt for payment for a room at a self-storage facility. The receipt doesn’t indicate room number. Employees  don’t recognize photographs of the suspect. The suspect isn’t connected with any other building, office, house, et cet., but is believed to have stolen property within his control. Suspect has declined to speak other  than to ask for counsel.

There are 100 rooms at the storage facility.

Is this probable cause for a warrant? How to retrieve the stolen property and obtain relevant evidence without violating someone’s constitutional rights?

We don’t think there’s an easy answer. But we hope to address this problem – and electronic analogues – in future posts. Comments and guest posts welcome.