LT3083 heat dissipation
If you output 2A @ 5v with a 15v input, there's your 20W approximately. So no argument there.

If you can keep the case exactly at ambient (22c), then you're looking at an junction temperature of 82c. The max specified is 125c, although I will say that I would not want to run it exactly at that point.

Now lets set the max ambient temp where the device will not malfunction as 32c (~90f). So now we're at a minimum junction temp of 92c, leaving 33c of headroom. This means your heatsink will need to dissipate 20W at 33c above ambient, giving a maximum coefficient of 1.65C/W  (33C/20W).

Now lets look at some heatsinks and see if we can get that.

A large pcb mount passive heatsink (2.5in x 1in x 1.65in) won't do it (2.6C/W):
https://www.digikey.com/product-detail/en/aavid-thermal-division-of-boyd-corporation/530002B02500G/HS380-ND/1216384

A little bit of airflow dramatically increases the efficiency. So if you look at heatsinks that come with an under-forced-airflow rating. You'll find many reasonable sized ones that can do it, for example this one:
https://www.digikey.com/product-detail/en/ohmite/RA-T2X-25E/RA-T2X-25E-ND/2416487
It's only 1in x 1in x 1.65in, and with forced air it has a temp coeficient of 1.5 degC/W

To do this with natural convection only, you'll need a huge heatsink like this one. In case the link breaks, it 5in x 5in x 1.5in: https://www.digikey.com/product-detail/en/wakefield-vette/394-2AB/345-1176-ND/4864910

And remember, these are only barely enough.