If that happened to me, I would have the engine checked out.
Did you notice the temperature moving up rapidly into the red zone at any point? I don't know the type of car, hence I don't know if you have an oil display. If not, the engine temperature can be a "pseudo-substitute" for the analog oil gauges that have been removed.
How long did you have th car running and how far did you drive it?
I would have it checked out; especially since there seems to be some "warrenty"--you mentioned "they are paying for it".
A little story from my grad shcool days when I was living in LA on 600.00 per month. I had a 77 Mustang that I did ALL work on. I kept that baby running for 300,000+ miles.
One day I drove into USC and parked in the structure. It had just been built, so the concrete had not been stained very much. When I came out that nite, I got in the car started her up and backed out. I noticed some brownish liquid in the space, so I pulled the car into another spot and checked. I located the source of the leaking water/coolant.....there was a very tiny hole in one of the core plugs that had rusted out. I checked the coolant level and it was a little low, but OK.
Flash forward 15 mins. I am on the Harbor freeway driving past some of the areas with bad gang activity. I notice that the temperature was increasing slowly. Then WHAM. The temp light went off the scale, the car was making horrible noises that I recall to this day. Got the car off to a surface street and called AAA. They told me it would be 45 mins to 1 hr to have a truck there.
While I was on the phone, 4 young teens were walking up to me and one was asking me some question. I know this sounds crazy, but I was trying to give AAA directions and I waved the teen away. At that point things got bad very quick. Two of the teens pulled me out of the phone booth and they all were demanding my wallet and watch. I was on the ground at this point, having taken two hits--one to head, other to stomach.
Just as I was taking the watch off, two motorcycle cops came around the corner. They saw me on the ground and hit the horns. The kids went scattering and my wallet was still on the ground. I had quit smoking for 6 months but I was so badly shaken up that one of the cops offered me a cig and I started up again that nite. I have never been so happy to see police in my life.
Lots of lessons I learned from this, but car-wise, I should have just bit the bullet and had it towed from the school. When I looked at the engine at the shop it was towed to, the little hole (seriously, it was about 1/4 the size of a pencil eraser) had turned into a BIG hole (the entire core plug disintegrated).
Engine had seized up. I tore into the engine and it was ruined. I went to a user car parts lot and found the correct engine and installed it. I got about another 45,000 miles off that engine before I sold the car.
To this day, I montor temp constantly and this is another reason I wish MB had not taken off the oil display. I am paranoid now about having an engine seize up on me when I am travelling at 65 mph.
Apologies for getting off track....Just brought back a bad memory.
My two cents worth.