Engine Overheating Alternator Power Steering Issues

[kdgX5]

I just had the alternator replaced last month on my 2001 4.4i X5. Yesterday while I was driving on the freeway and after accelerating quite rapidly to merge with traffic, I noticed a burning smell. A few moments later the alternator light and coolant temperature warning light came on. While pulling over to let the engine cool down I noticed that I had no power steering. Also the heat is not working at the proper temperature. Nonetheless, the engine cooled down quickly. I was able to drive for another 10 minutes until the engine overheated again. Luckily with frequent stops I was able to get home without blowing up the engine!

The next day I checked the coolant levels; reservoir filled. Oil filled, etc. Although the alternator light was on, the car started just fine in the morning.

I am curious to know if anyone has had a similar issue with their X5? And, if so what was the problem?