Which would be less detrimental to short-term storage (< 5 weeks) of "average" red wine:
A standard food refrigerator, probably about 40 degrees, or at hotel room temperature of about 70 to 72 degrees?

Also, does refrigeration at 40 degrees or colder permanently damage the flavor?

Thanks!

Either is fine for that duration. But it'll probably take longer to warm your red wines to serving temperature coming out of a fridge than to chill them from room temp, if that makes a difference to you.