I know monofilament takes on a set from the reel spool especially in high heat situations like a vehicle sitting in the sun for hours day after day.  How does this heat affect other lines, especially the braids?  What sort of line do you use for a trunk rod combo?

I don't leave gear in the truck at all.  It goes from garage to the truck to the boat and back again.   As far as line goes, I think heat would effect braid the least but it would depend on how well fused it is and how old.   The one thing they tell you to get line to last is to store it in a cool dry place out of the sun. 

Braid should be fine. I used to leave a two piece rod spooled with braid to leader in my car, never had any effects. Now I don't leave anything in the car, unless on vacation. 

I've left a 2-piece spinning rod and casting rod in the trunk of my car over the summer.  Both spooled with braid.  Didn't hurt the line to the best of my knowledge.

 

Used to carry a rod spooled with YZH copoly in the back of the truck. Stayed there all the time including Texas heat > 100*. Kept it under the rear seat. Never any issues. I think UV is the primary killer of lines, not heat.

I think heat will definitely mold some lines to the spool so the use of line conditioner products is always a good thing but I don’t imagine laying on the deck or rod locker is much cooler and you have the added uv damage.  Braid shouldn’t be affected unless it is brand new and still has a heavy amount of whatever type of waxy product they coat it with.  I really dislike braid until that coating is worn off.  

I don’t know how hot it is where you live so you’ll have to take my response with a grain of salt. I use mono a lot. I live in the Pacific Northwest. Our summers can hit 90 plus but nothing like Arizona and other like states. 
 

Incidentally, I’ve also used braid and fc and they too have never been affected by heat in the trunk. 
 

My rods can be in the trunk months at a time and I can’t recall heat ever affecting my lines, mono or otherwise. I think there is a difference between heat and UV rays. The latter can affect mono over time but I usually replace the line before that can ever happen.