How unsafe is meat that has been left out?

I bought good quality stewing beef this morning that was shrink wrapped. When I got home I accidentally left it in my bicycle basket outside. I sat for 3-31/2 hours in the heat. It was wrapped in a plastic bag, so it was not getting direct sunlight. When I discovered it it was very warm too the touch, but not out and out hot/cooking. I instantly threw it in the freezer to get it a shock of cold, and then moved it to the refridgerator. Obviously, it isn't 110% safe at this point. But does anyone have a realistic idea of how safe (or unsafe) it is? Before refridgeration, surely not all meat was eating or cured within minutes of killing the animal. So, I don't want to pull a typical American, USDA freak out and be wasteful. But I don't want to be downright stupid either :)