Howdy,
Welcome to the wonderful world of Composting ;-)
As you have learned , Grass (as well as all green goods) will get your pile very hot, very quickly.
Don't add dirt to your compost pile, it doesn't compost and it doesn't really add anything to the composting process.
Keep adding Greens and keep turning , it will give you lots and lots of soil amendments for your efforts ;-)

You can add fertilizer, but it's not a real wise monetary move.But if you have it on hand and you are "chomping at the bit" to see your whole pile heated up, go ahead and do the science experiment, it'll only set you back a few bucks and you can have all of your neighbors and family and friends come over and stick their hand down deep into your pile and show off your steaming bins ;-)

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Your compost gets hot because of bacterial activity and they need close to the 30:1 Carbon to Nitrogen ratio and just enough and not too much moisture in the mix to do that. Because grass clippings are quite high in Nitrogen, as well as moisture, they did help. Adding the fertilizer might if there is the right amount of moisture present. As long as you have the fertilizer and if you donot plan to use it anywhere else your compost could be a good place fo it.

I think high nitrogen and protein things really get the compost hot. A load of fish carcasses does the trick, but meat's maybe fun for later!
Grass clippings are my default starter as they're easy to access (make sure they're well mixed into the rest of the heap, or they stick together in impervious layers.
Manure's great.
Comfrey and high-protein legumes like alfalfa.
I wouldn't use fertiliser. You don't say if it's 'natural' or synthetic, but synthetics will do a number on your bacteria. I can't speak for 'natural' ferts, but I'd be wary of that in the compost too. Seems like a waste of money with so many awesome cheap or free compost goodies everywhere!

You might want to spend some time with the web site linked below. Many people have used synthetic fertilizers as catalysts for compost with no adverse affects. Probably if a synthetic fetilizer made up a very large part of the compost it might have an adverse affect, but since you already have it on hand there is no good reason to not use it.

Here is a link that might be useful: Compost Tutorial

Hey I almost forgot that I asked this question. Thanks to everyone that replied. I checked my pile again today and there was some really good heat come from nearly every spot I checked.

Still, I am confused about one thing and that is if I constructed my bin the right way. I used old pallets and pulled off each board until I had enough for a 3x3 structure. I did not leave gaps between each board so the compost bin is enclosed on 4 sides, sitting on open ground and I made a top to go on it. The top does have a 2" gap on each side for air flow but is this enough? Should I have left gaps in the boards on the side as well?

Obviously it was old wood and there are tiny gaps here and there but I am not sure if this is the best situation or not.

Thanks everyone

"...I am not sure if this is the best situation or not. "

Not to worry. You will have to turn the pile periodically. Air (nitrogen/oxygen) is needed on the inside so anaerobic conditions don't develop. A good bin design will let you do that easily.

Some folk conjure devices to introduce air, but at some point unreacted outer material needs to be turned in regardless.

One of the advantages of a tumbler.

I did my pallet bins with the pallets in their origional form, and then stapled some of that plastic chicken wire to the inside surfaces of the pallets.

I have been turning my pile about once per month and continually adding anything I can get my hands on. Sticks, leaves, veggie scraps, grass clippings, weeds from pulling, garden plants that have been pulled. I even got two large scores when I had a few stumps ground, and then again when the power company had to cut a tree away from a power line at a neighbors.

I don't see any steam in the morning, but I suspect I will when it gets a little colder in the mornings, and my pile has been shrinking continually. I have filled the bin to the top about 4 times now and it keeps shrinking down to about half full each time after a few weeks.

I also have an apple tree and have been picking up all the fallen apples and throwing them in there as well.

Anyway, the whole point was that mine does have more air slots, but if you look at Johns above, his is concrete block, so there is no air slots. I think though you would be better off turning slightly more. Maybe once per week would speed things up for you.

Try it out and see how it works.

I have had bins, much like Jon Hughes, made of stacked concrete blocks with no "gaps" and never had a problem with air circulation. My current bins are made of cedar boards placed tightloy together with no air gaps, at least none I deliberately put in, and there is no air problem.
Piles less than 6 feet wide and high generally will not have a problem with air circulation.

Sounds great, everyone. I have also been piling anything and everything in there just trying to build it up as fast as I can. I love putting my hand in and feeling the heat come from the pile. Its kind of exciting really!