Well, that is exceptionally short, but even with that modern cars both warm up faster and control fuel to the point that they don't wear out like older ones do. Even a 5 mile commute gets them up to full operating temperature, even if that's not quite long enough to get rid of all of the water in the oil or exhaust system.Not just hard on the motor/transmission but also not being able to get up to operating temperature for half the trip must add heavily to emissions and shorten the life of emissions equipment? I take an almost daily trip to a UPS store for our mail and to make shipments for our business. It is only 1.1 miles away through one long traffic light. Not much of a warmup for an ICE vehicle.
As I implied above, one of the reasons I'd like an electric car is to be able to warm it up from a smartphone app while having my last cup of coffee. Well, that and not gassing up in winter!