As an aside, compost should not be allowed to go above 165 degrees F or you are killing off the good microorganisms. It should be turned at or before that temperature. This ensures the pile remains aerobic and healthy. With compost you're trying to add good life to the soil and give these soil microbes great things to eat.
We don't know if you're wanting to plant in these raised beds soon or at a much later date. The suggestion of adding high-N matter to keep the compost going assumes you're going to use the beds later, not sooner.
If you're not willing to rake it up and compost it further, and want to plant in it soon, then you really just want it to decompose slowly, not quickly. You don't say why you think you need need some mineral substance to add. You can seriously throw off the soil's mineral balance by making uninformed decisions and adding material. Boron toxicity comes to mind. Trace elements have to be in trace quantities.
Without a soil test, no one can really
answer your question on what more needs to be added. If you just want to make your best guess with no real data, I'd say cover it with 6" of good topsoil, don't till the still-hot compost into the topsoil, and plant in the topsoil. The
roots will decide when it is safe to push into the compost. But really, if the compost is not mature, no plant will want to grow in it. Eventually it will be conducive to plants, earthworms, etc. They can do the mixing for you, so you can save your back.
There's really not
enough information to answer your question, but maybe this helps.