Turns out the cause of the whining is the driver not the heater fan :)
After getting your encouraging advice I removed the panel on the heater inside the camper to find a panel of electrical wiring and a brass gas pipe that I was reluctant to fiddle with to get access to the fan, so decided to wait and have a pro look at it.
But that night temperatures fell below freezing so decided it was better to see what happened when I turned the heater back on than risk freezing and cracking the water pipes, since even though the pipes have insulation around them am not sure how much cold they can tolerate.
Much to my surprise the heater started up with an enormous shriek for a few seconds, then started to purr as it normally does with only a little whining. Since then I have travelled further north to Moab then Mesa Verde with bright sunny days but cold nights with temperatures hovering between freezing and a few degrees below but no problems with the heater apart from an occasional squeak that reminds me of the noise the old fan in my desktop computer used to make before I replaced it. So I figure most likely a good idea to have an expert look at the fan some time ahead when that is convenient but meanwhile no risk of destroying the heater unless the fan conks out that will be easy to notice as it will stop blowing hot air into the camper.