The dynamic jaw does move a little each way, but it is very hard both in and out. I will get some kroil and give that a shot.
Don't bother with heat....you won't be able to put enough into it where it matters to do anything. I've tried and it's simply a waste of time. There's too much mass and it soaks up the heat before it gets to any rust.
One critical factor in getting a Wilton unstuck (and most others) is that it absolutely has to be securely mounted to something that won't move. If not, much of your effort is completely wasted and you won't get it free.
Since it moves a bit, bolt it to a bench and then try prying a bit between the jaws if you can get something in between. There's a good chance it will pop free. Then just wire wheel the slide clean, run rags into the body of the vise to clean it (a bit of carburetor cleaner works well for that), then grease the slide and reassemble. I like marine trailer grease because it displaces water well, is usually green that goes well with the Wilton color, it's easy to find, and is pretty inexpensive.
If that doesn't free the dynamic, you need to really disassemble it properly. Run a dowel through from the front, pop the dust cover out, remove the rear pins, pull out the nut, then use your dowel again to knock the tail cap assembly out. That will allow you to use a large socket, or piece of pipe on the back of the slide and tap it free (with the base secured to a bench). Clean, lube and reassemble.
It looks like your vise was "restored" by someone and depending upon how well it was done, they might not have gotten the slide or body of the vise really clean and sitting for a couple of months was all it took to seize it. A spot of rust half the size of a dime can lock up a Wilton solid.
I run through the process here, and it also has a link to a video about the easiest way to remove rear pins.
https://mivise.com/vise-restoration-process/