With an automatic, this would be easy. So easy that it's already done in most cars.
Manual is a little trickier. That thick oil will only slowly warm up, and you will have to wait for the coolant to get warm before it starts heating it up anyways. Trying to run coolant lines back to your tranny to warm it up seems like a Rube Goldberg device that will likely end in leaks and no measurable gains with your short commute.
Replace the dyno squeezings with a decent synthetic oil and call it good. Add electric heating if you are running it elsewhere (coolant, engine oil).
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