Doesn't fit the data - if he's already been sleeping, his bed will be warm, and he wouldn't have the incentive to get up and change beds.
So, it is likely just a matter of getting him comfortable sleeping somewhere warm so that he isn't interested in moving to our bed.
Edit: Having said that, before I started this routine, he _would_ come up to bed if he was sleeping somewhere else already on a normal night in. So, I don't know.