My copy of Buck Tilton's Wilderness First Responder notes that for cold water immersion, aside from providing standard treatment for hypothermia, the patient should be "handled gently, lifted from the water, and kept in a horizontal position". Dry them off, and insulate them from further cold before you think about building a fire. (The reason behind keeping the patient flat is to avoid stressing their heart.)
If you fall in yourself, use the first minute to get control of your breathing, then assume you only have about 10 minutes of useful muscle activity. Use that time to pull yourself out or swim to safety.
In terms of re-warming, the vast majority of the work will be done by the patient's own body: your role is to support that by minimizing their external heat loss and topping up their fuel supply (calories) if they are conscious. Adding external heat sources may help a small amount.
Now, there is some contradiction between the need to get someone into dry clothes and the need to keep them insulated from the environment; obviously if they are in the open with howling winds and rain it's probably a bad idea to pull off their clothes. So, let's look at some other protocols that may be better suited for the solo traveler or those who were only briefly immersed (e.g. fell in and climbed straight out).
For this I'll reference a "re-warming drill", which you can read an example of at https://www.sitkagear.com/insight/a-navy-seal-rewarming-drill. This method relies on both body heat (as previously mentioned) and also proper gear selection: wicking fabrics and synthetic insulation. If you don't have the proper clothing, it's not likely to work very well. The type of clothing system mentioned in this article may be referred to by many different acronyms; searching for ECWCS or PCU should give good results.
In the first form of the drill, the troops pair off and immediately add synthetic insulation layers. One person sets up the tent, the other sets up a stove and gets snow melting or water heating. With that done, both burrow into their (synthetic) sleeping bags. As soon as they can, they then get some hot drinks and calories into them and lie back down.
The second form of the drill addresses the case of what to do without tent, sleeping bag, or stove. In that case, the troops simply put on their synthetic insulation layers and their packs, and then marched for a few hours at a slow, easy pace (enough to generate heat, but not to sweat).
Having described a pair of options, you can also look at the Wilderness Medical Society Practice Guidelines for the Out-of-Hospital Evaluation and Treatment of Accidental Hypothermia section on field re-warming. It suggests that patients not be immediately allowed to stand or walk, and that delaying exercise for about 30 minutes will help reduce the risk of afterdrop.
On a personal note, I haven't yet decided to jump in an icy lake, but I can attest to the drying abilities of modern synthetics. This past summer, after getting my hiking pants largely soaked in a thunderstorm, I added GoreTex pants over them and after a moderate amount of walking had completely dried them out.