Shrink fit steel pin into an aluminum piece

You may have a press; aka lathe tailstock. A milling vise would also, not a bench vise.
Cold pressing; I haven't seen any mention of surface finish. They need to be well finished, particularly the aluminum. It will gall and displace the pin position. The steel pin should have a small polished radius to burnish the entry and passage through as it seats.
Shrink Fit; Temperature wise, the calculations are reasonable, but small parts want a fixture to assure a one shot drop. If that's blind hole, a vent will help. Any excess force, ie hammering, heavy pressing, or off-perpendicular press can deform the pin, negating the project.
There are reamers for odd sizes, nothing but a micrometer and a couple appropriate wrenches needed. Standard reamers are common in .0005 steps, a dowel pin set might include .0002 +/- to generate selective fits; slip-press-interference.

Better yet;
One type works on through holes, the "adjustable blade reamer" https://www.google.com/search?client=firefox-b-1-d&q=adjustable+reamers The separate blades ride in tapered slots, positioned by a pair of nuts at each end. They are the most capable of very small increments of change. This is also rather predictable, by counting the thread pitch and turns to gain a specific change.

Another through-hole type, is the expanding body reamer. It pushes a tapered pug inside a relieved body, resulting in a slight egg-shaped condition.

The third variety is expansion reamer also, but suited for blind holes. The reamer looks conventional, closer examination reveals cuts in each flute, a tapered set screw enters from the cutting end to modify the size.

It's best to insure changes of ANY adjustments by test, and insure cutting elements are fully seated.

There is a trick of shimming a reamer with a tapered brass leaf; it's easily demonstrated, not so easily described in text.
 
You may have a press; aka lathe tailstock. A milling vise would also, not a bench vise.
Cold pressing; I haven't seen any mention of surface finish. They need to be well finished, particularly the aluminum. It will gall and displace the pin position. The steel pin should have a small polished radius to burnish the entry and passage through as it seats.
Shrink Fit; Temperature wise, the calculations are reasonable, but small parts want a fixture to assure a one shot drop. If that's blind hole, a vent will help. Any excess force, ie hammering, heavy pressing, or off-perpendicular press can deform the pin, negating the project.
There are reamers for odd sizes, nothing but a micrometer and a couple appropriate wrenches needed. Standard reamers are common in .0005 steps, a dowel pin set might include .0002 +/- to generate selective fits; slip-press-interference.

Better yet;
One type works on through holes, the "adjustable blade reamer" https://www.google.com/search?client=firefox-b-1-d&q=adjustable+reamers The separate blades ride in tapered slots, positioned by a pair of nuts at each end. They are the most capable of very small increments of change. This is also rather predictable, by counting the thread pitch and turns to gain a specific change.

Another through-hole type, is the expanding body reamer. It pushes a tapered pug inside a relieved body, resulting in a slight egg-shaped condition.

The third variety is expansion reamer also, but suited for blind holes. The reamer looks conventional, closer examination reveals cuts in each flute, a tapered set screw enters from the cutting end to modify the size.

It's best to insure changes of ANY adjustments by test, and insure cutting elements are fully seated.

There is a trick of shimming a reamer with a tapered brass leaf; it's easily demonstrated, not so easily described in text.
Thanks for the helpful and interesting post. Makes the process more understandable. It would seem that fixturing would be necessary to achieve success (as usual!).

I do have a milling vise that has a bit more jaw lift than I'd like, that I'd be willing to try as a press. Hammering just doesn't apeal to me. Too easy to get off axis or mushroom the pin. Looks like one would need a piston attached to one jaw and a socket to receive the protruding pin. The socket should be a sliding fit but not loose, with a vent hole to allow air to escape. Piston should be steel it would seem, and perhaps also the socket, both so they last for multiple operations.

How does one initially align the pin if the vise is on the table, any fixture would be in the way? My limited imagination is thinking of a vee guide. I suppose one could remove the guide once the pin is started, but that might disturb the setup. A cupped piston would work but then the piston cup would have to be changed out to drive the piston below the surface (flush is ok).
 
Another idea...

Countersink the hole on the back side.

Make overall hole size slightly smaller I'd than the active part of the pin.

Pin now has full diameter where it is used with a smaller diameter where it goes through hole, it has a shoulder to hold it.

Make the fitas tight as you can, requiring hammer tap to insert improves outcome.

Fixture in something strong and heavy, like drill hole in chunk of steel same size and depth of pin.

Get the biggest hammer you can find with a pointed punch, same angle as drill bit, place pin in hole, bracket on pin, punch on pin and drop hammer on it.

Hammer blow will be far more than possible with vise or likely available press.

Small hammer requires much more effort, very large one just a tap.

It should deform to fill countersinkbeyond. good.

Could add locktite or epoxy to provide additional hold.

File off the high stuff for better fit if needed.

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No need for a jig if you use your mill vise. Take up the vise slack, then align by eye, both horizontally and vertically, then crank away. A 0.300" thick piece of Al will pull and keep the pin straight if it is even close at the start. As for mushrooming or the head, you'd be hard pressed to even deform the pin using the vise, or even hammering. When you hammer in a nail, does the head mushroom? No, it doesn't.

Another way to start is to tap the pin in with a hammer (see above if you're worried about mushrooming the head), then use the vise. My feeling is once you start tapping the pin in, you will notice how easily it is going in and continue tapping with the hammer until the pin is seated.
 
No need for a jig if you use your mill vise. Take up the vise slack, then align by eye, both horizontally and vertically, then crank away. A 0.300" thick piece of Al will pull and keep the pin straight if it is even close at the start. As for mushrooming or the head, you'd be hard pressed to even deform the pin using the vise, or even hammering. When you hammer in a nail, does the head mushroom? No, it doesn't.

Another way to start is to tap the pin in with a hammer (see above if you're worried about mushrooming the head), then use the vise. My feeling is once you start tapping the pin in, you will notice how easily it is going in and continue tapping with the hammer until the pin is seated.
I'll find out in a bit. Got some computer problems I'm trying to resolve first. Basically have no access to my CAD design files at the moment.
 
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