i tend to put most my sauces in the fridge after a while, depending how often they get used, because otherwise they'll go bad and have to be thrown out (even though they are themselves basically preservatives, the effect isn't perfect). Some pickles too.
ketchup goes in, because there's not a great deal of things i actually use it for. it's been a bad summer for bbq's, so it generally ends up going in marie rose for oven-cooked breadcrumb fish instead. as the mayo for that is chilled anyway, it makes no difference.
if it bothers you that it's cold, just leave it on the counter for 15 minutes before serving. get it out when you start cooking / before you go to the drive thru. or buy in a load of the single-serve sachets.