Well, you cold invest in a bag of alfalfa pellets and mix those in. But at this time of year, it should be easy to find some fresh, green grass clippings to mix in.

My problem is having the pile heat up to 160 degrees, then drying itself out.

My experience is that the volume of material is not sufficient to sustain the bacterial activity needed, your pile is too small. A 4 x 4 x 4 size is more likely to hold heat, or bacterial acitvity, longer. I'd not add any more Nitrogen.
The tarp may be limiting the necessary air exchange, imprevious material over or around a compost pile is not a good idea.
There is some new research that indicates that it is not the heat of a compost pile that kills the "weed" seeds but the length of time they are in the compost pile that does that.

It sounds like your pile did reach a good temp very well. Like perhaps there was too much N back in the beginning. And then as you said when you added more browns, it got hot again. How long do you really expect it to stay hot? My compost pile stays hot (in the active top center of the pile) because I keep adding to it but the lower parts of the pile are allowed to cool and age as they will.

Here is a link that might be useful: My Garden

I like a round 4' diamater bin. I find that if it rests directly on the ground, it only needs to be 18" or 24" high to have good heat retention. There are a few sites that still recommend putting the pile on top of a bunch of wood branches (I assume for air circulation). But putting the pile directly on the ground means the dirt can store heat, and it will be easier for the worms to move into the pile when the heat drops off.

When new ingredients are added to an existing pile, usuaully the second and third temp peaks will not match the first peak temp when all the ingredients were fresh.

Kimmsr said "There is some new research that indicates that it is not the heat of a compost pile that kills the "weed" seeds but the length of time they are in the compost pile that does that."
What I've been saying all along. The pile provides good conditions for the seeds to sprout - warmth, darkness, moisture - which are bad conditions for them to grow. That's if you keep a thick lid of 'browns' on top.

I agree it's not a good idea to keep the pile covered with a tarp. There's a chimney effect in a healthy compost pile - it draws in air from the sides and vents it out the top. The pile needs to breathe.

I would leave the pile to compost, since you have time to let it do that.

Thought I would update on what is going on now.........

I stirred things up and wetted it down a bit more, and after a week, still nothing. So I broke down and did all that made sense to me--- I added more Nitrogen!! I knew that there was a ton of chicken poop in there/grass clippings/kitchen waste--- but also know that is what you add when you are trying to heat up!

So I bought a box of EB Stone Compost Maker (first time ever, but thought, what the heck--- it will add stuff that I don't have access to (bat guano!) and other fun stuff).

Well I did that 3 days ago--- basically tore the pile down, built it up again, making maybe 8 layers of the compost and the Compost Maker and wetting it down a bit (edges were dry but middle was moist).

WaaaLaa....3 days later the compost pile is 100* !!

I did take the tarp off, and feel that had something to do with it, too. I have NEVER put a tarp on before, but was reading in several OG books that you should cover the tarp to keep in moisture and heat, and so figured I would try it. That obviously didn't go well for me.

So thats where we are for now. All in all, the $5 I spent on the Compost Maker was worth it for me.

:)