You might want to dilute it by adding a lot of other materials to it. If all you are adding is kitchen scraps, you need some browns anyway. Without browns the kitchen scraps may get smelly from too much nitrogen. The high pH will exacerbate this by driving off ammonia. Mix in dry leaves or other vegetation, shredded paper, sawdust or wood chips. Eventually it should balance out. If you have a lawn, and your soil isn't alkaline already, you can spread a lot of ashes on a lawn and still have a very thin layer. Just sayin'.

Meats (including poultry, seafood), dairy, bones, fatty foods such as peanut butter, mayonnaise, lard) diseased plants, human or pet feces (including kitty litter) should not be added to a compost pile.

I tend to agree with Kimmsr. You might want to wait until winter begins to wane a bit and then add some urea and turn the pile and then add some more and turn again. My piles here is Missouri 6a are usually frozen on top in the winter but this year has been pretty mild so far with no lows below 20 and daytime highs above freezing. That will end this weekend when we are supposed to get single digit lows for a day or 2. I don't think my piles are hot right now but they appear to still be shrinking slowly. I will wait until late February or early March and then merge my 5 fall started piles together into 2 or 3 while adding urea at the same time. When the grass starts to grow I will start building some new piles using 20 or so bags of chopped leaves I saved from fall, fresh grass clippings, and a few 5 gallon buckets of chicken manure that I accumulate over the winter.

+1 with the top layer of leaves. I do my pile in layers, using a water can to wet each layer as I build it. I will admit it takes a knack to build it that way but I can get it hot in a day or 2. I don't turn my piles either. Once the pile is hot I make a hole in the center for any new kitchen scraps, again covering over the top with leaves. While the pile is cooking I need to add water almost daily. This may not be the best way as it doesn't cook all the weed seeds on the perimeter of the pile, so I try to put anything with seeds in the hot center of the pile. Once it begins to cool down I may turn the stuff from the outside in but then I may not. Depends on me and/or the weather. Now for the reason - the reason I don't mix it all up in the beginning - besides being a lot of work is that mixing up so there are kitchen scraps scattered thruout the pile not only attracts rodents but insects which can be hard to get rid of. As mentioned covering the top with a layer of leaves keeps the insects away. I do have one bin made from hardware cloth that will exclude any rodents but I find it impossible to exclude insects. Also you should have a way to cover a pile when it rains or that can slow it down or stop it completely. A tarp or an old shower curtain will work just make sure you have something to hold it in place.