Piece Of Cake
I am a victim and now veteran of the Ford 4.6L, 3 Valve spark plug removal, via my wife's '06 Explorer.  Believe me, the Town Car spark plug replacement is child's play! 
 
Take a look at Ford's TSB for this problem design spark plug removal, compared to how real mechanics now get the job done.  
Ford TSB 08-7-6 SPARK PLUG REMOVAL INSTRUCTIONS—4.6L 3V/5.4L 3V/6.8L 3V
Ford 4.6L & 5.4L 3V Spark Plug Removal
by FordTechMakuloco
Ford 5.4 Liter 3 Valve Spark Plug Removal 
by srmastertech, Ford Senior Master Technician
The real fun starts when a portion of the plug breaks in the head.  Ford's procedure for removing those remnants is exceedingly cumbersome.  
Lisle now makes an extraction kit that gets the job done in a similar fashion, but much quicker and easier.   
Ford had a good design for getting more horsepower from this engine, but the special plug required had this bug.  Later engines use a larger bore for the plug extension, as well as the new designed, one piece plug.  In the mean time, Ford released a TSB for the problem, which worked... sometimes.  Over time, mechanics found better ways to do it.  In other words, Ford's TSBs are not written in stone, and are fallible. 
Your Town Car's plugs are a piece of cake.  Being aware the steel plug can gall the aluminum threads is the main concern.  Hot, warm or cold, I suggest cracking the plug loose, spraying lubricant in the well, move on to the next plug, crack it loose, spray and continue.  By the time you return to the first plug the lubricant will have soaked down the threads.  Work the plug back & forth for a turn or two, and you'll find you can spin it out by hand.  You'll know it isn't being galled at that point.  If you need to wrench it more than a turn, work it back & forth with more lube till it can spin out by hand.
By all means, do what you're comfortable with, or let your mechanic do it.  While you're there, ask him if he's going to wait overnight to work on it.  
