I'm no expert, but there's probably some electronics in that arm whose operating temperature range is a lot higher than the temperature of space.
Of course, if there's a CPU in there that's drawing lots of power (e.g. image processing), it will have to shed that heat. But if there's only some electronics in there that don't eat up too much power, there's a good chance they'll use the thermal blanket (and even heaters) to keep them warm.
I don't have the details on the Canadarm, but I can tell you that a lot of electronics on satellites use thermal blankets and heating elements to keep warm.