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So my question is if I pitch the yeast at 80 degrees and put it in my mash room. It's about 71 degrees in there now cause of the AC will that hurt my fermentation. Or slow it down

Depending on what yeast you are using, it will slow it down. I know I use DADY yeast and it slows down in that temp range.
There are other beer yeasts that don't mind tho. It really depends on your choice of yeast.

Did you calculate for the amount of heat the yeast are going to raise themselves?

Good point, I wasn't even thinking about that. They do create quite a bit of heat themselves.

I'm going to use bakers yeast cause well that what the wife has right now I was thinking about wrapping it in a blanket

Wrap it up. Bakers yeast does not like being cold.

I built a box in a corner (top and two sides) out of cheap OSB in my heated garage 66F. It really doesn't need insulation, but you can if you want. I put a electric heat controller in there with a small space heater as well as a fan that kicks on to recirculate the air when the heater kicks on. I set the temp to 75F-78F initially. Over the first few days my 45 gal wash's temp will be 82F because it generates its own heat. Later the temp in the box needs kicked up to 84F or so to maintain the wash's 82F-85F or so. I check the wash's temp once per day. While I'm at it I also check the PH. If I want to keep really good notes, I'll also check the ABV. I use Fleischmann's yeast and its ideal temp is 85F.