The recommendation of 195°-205° isn't necessarily "ideal". In fact, with the long extraction time of a French press, you might get better-tasting coffee with lower temperature water.
The inventor of the AeroPress tested different water temperatures, and settled on 175° (for dark roast to 185° for lighter roasts) as what almost all of his taste testers preferred. The one exception preferred 165°. The higher the temperature, the more extraction there will be of bitter-tasting flavor components.
In my own tests with medium roast, I noticed a big improvement starting at 195° instead of between just off boiling and 205°. Starting at 175°, I had to extend the extraction time a little, and the flavor was noticeably more acidic and less bitter. Starting in the range of 180°-185° gives me nicely balanced flavor with little bitterness.
For fuller flavor at lower water temperatures, you can use a grind a little finer than the coarse setting typically used for French press. I get good results using even a medium grind (close to what you'd use in a drip coffee maker), with 180° water and total water contact time of about 4-5 minutes before starting to decant.
Don't worry about the temperature dropping. You could insulate the carafe, as STL Road Warrior suggested. But even if the temperature drops to 150°, it will still be extracting, just slower and with less extraction of bitter flavors. Much of the acidic flavors will already have been extracted (they get mostly extracted early). At those lower temperatures, the bitter compounds take much longer to extract. So if you extend the extraction time while the water temperature is dropping, you get fuller flavor without excessive bitterness.
In fact, one technique is to skim off the crust at about 4 minutes. That gets rid of some of the bitter-tasting oils and fines. Then let it sit for several more minutes while most of the fines settle out, and the coffee gets closer to drinking temperature. Going this route, people sometimes don't plunge the screen through the brew and stir up the fines again. They just leave the screen near the top of the carafe and filter through it as they pour the coffee.