Consider the use of RFID temperature sensors. Each one would have a unique ID, completely wireless, no power needed. And they would follow the frames around regardless of where you put them. You pretty much just encapsulate them and drop them wherever you want.
You may need a RFID reader per box, though because the range of RFID is generally limited (however, there are ways around that.)
http://www.phaseivengr.com/p4main/Sensors/WirelessTemperatureSensors.aspx