using fresh-ish cow muck in the garden

We have poor, stony, compacted soil. I just managed to get about 8 tons of cow muck delivered, some of it is a few months old and some is fresh, all mixed together. Shame I couldnt have gotten it a few months ago, but that's what I have. I've planted about 1/3 of the garden and working to prepare the rest now for planting over the next few weeks-month. The things that I am planning to plant are runner beans, cabbage, cauliflower, sunflowers, strawberries, parsnips, and other stuff as I can fit it in.
My question is can I use the muck now in any way? Should I dig it in and let it rest a few weeks? Just put it on the beds and leave it alone? Top-dress the beds once they are planted? Or leave it to compost until the end of the season and then dig it in then for the future?

Does it look like it is composting , giving off any heat?

It is hot at the moment, it was just delivered two days ago. It was steaming then, it's not as hot now, and the guy said he expected it would stop smelling (smells a little but not too terrible) within a week or so.

I'd put it on the future beds now. If it composts in situ, so be it. It won't do any harm added in a layer on the ground. I'd let the rest decompose a bit and add it to existing beds only after it cools down. I'm far too lazy to dig anything in, especially eight tons of it!