You could do something really clever and repair the heater box's. If your box's are rusted/burned out where they connect to the muffler ,you can buy a little repair kit to replace the ends only. New heater box's are terrible. They do not fit well and don't heat well and cost way to much money and they have to be for a bus/van . Box's from a bug are different in the way they are hooked up to the levers.
     You can block the air pipes shown in you pic, but make sure that the plugs will not fall out. It would cost you about 50-60% of your engine cooling air. Not good and just in time for summer driving.
      You might check under the van and see if someone wired the heaters on for winter due to broken cables. If so ,cut them loose. A very common thing to do. I hope this helps.

Do what to make a exchanger overheat. ?Melted what plastic? If the heater boxes are in normal, good operating condition and turn them off with the cables there is no air passing through the boxes. The air is stalled out at the flap inside the box. What would make them overheat ?  If you are melting something you have problem.  If you pull the flex pipes off the heater box under the car and the heater box flaps are still lock open you will loose a lot cooling air. That be like taking the pipes off the fan housing and leaving them open. Not a good thing for summer driving around here unless you just love to burn up stuff.
       The bottom line is------Repair or replace your heater exchangers and be done with it. :roll:

As long as you are happy :roll:

I've never seen one get hot enough to melt anything, but they will get a little hotter with the air to them disconnected.  When you close the flap to cut the hot (  :lol:  ) air off to the cab, a small amount of air continues to flow across the heat sink and out the vent behind the flap.

The plastic that melted was the little vent that is in the kick pannel on the back seat.  The heat oozing out of the heat exchangers killed it.  It was just a convection heating last summer.

I think the key to Casey's problem was the time of year it happend.  I wire open one of Homer's heater boxes in the winter (the other one is bad) . . .  If I wear good gloves and it doesn't get below about 25 degrees, I can make it to work without have frostbite on my fingers.  In July, stuff on the dash starts melting and I have to close it off.  Even a heater box with rusty outer tin will put out WAY TOO MUCH heat when it's 100 degrees outside!  If you have the fresh air tube disconnected AND your heater box flap isn't closing all the way, you can draw air through the heater box moving down the road . . . it won't be a huge volume of air, but if it's 100 degrees going in, you can bet it'll be even hotter coming out!  Now if we could just figure out how to get 'em to put out that kind of heat in the winter . . .   :lol:

Perhaps, but was the last pun really necessary?

 :lol:

I slid under it when I got of work today and could see where the previous owner had used old coat hangers to rig the heat exchanger on all the time. When I unhooked them I was able cut off the heat. I used a heat shield exhaust tape I had left over from my motorcycle to help seal some of the leaks around the heat exchanger and it appears to have stopped almost all of the exhaust smell -heat. I appreciate everyones advice.