On cold days I like to drive the first 3-4 minutes in low gear - keeping the RPMs at 3500-4000.

This makes the heat come out warm much faster. If I drive normally, then the heat will not come out warm in the 10 minutes it takes me to get to work.

Is doing this harmful to the engine or tranny?

It's not a good thing to do. Maybe the link below will help:

https://www.askmehelpdesk.com/cars-t...tml#post262690

You could make your own "winter front" and it might help somewhat during your short drive to work.

Keep your oil changes at 3K or less with those driving habits. And I agree with tx!