Went for my oil change and when I went for the drive home some little ricer wanted to race so I was all for it, haveway through the run I smell coolant and there was smoke coming out and my temp was getting close to the red all of a sudden so I stopped right away at a friends house that was a block away. When I went to look under the hood I noticed that the cap for the coolant was gone( was there a few days ago). So I bitched and yelled at the people for a good 1 hour or so and they cleaned up the mess, free car wash and oil change for a year. What type of damage could I have? It didn't go into the red but was close. They said if anything isn't running right to get it checked out and they'll pay for it all.

 

If you have no leaks then you're ok, if it got hot enough to warp a head or do some damage you'd be leaking coolant or oil real bad.

This is a prime example why I do everything myself if I can. I've heard of people driving off and someone forgot to put the drain plug back in tight and it fell out draining all of their oil and ruining their engine. Sounds like they are being real cooperative with you on it though, but I wouldn't let them do anything that you can't do yourself.
I don't even bother taking my car into the shop if its under warranty and I can do it myself...by the time I fool with taking it up there getting a ride back home and then finding a ride back to pick it up, or waiting, I could have done it myself.

 

When i used to work at a insurance company youd be seriously suprized how many claims was seen from a oil change place forgetting to put the oil plug back in the car or even forget to put oil in a car.