Help: procedure to check coolant system

[conix67]

The electric coolant pump died on me a week ago, and my Indy service shop replaced it along with the thermostat. Long story short, the new pump didn't work so got a replacement from BMW. However shortly after we found out the new thermostat was also defective and engine was overheating. My mechanic told me something like this never happened before.

Now, I'm totally paranoid about this and would like to check if the cooling system is working as expected at least daily. I plan to obtain cheapo Bluetooth OBD2 module to get live data readouts including coolant temperature. Until then, what are the best methods available? any suggestion is very much appreciated.

Also, I noticed the radiator fan starts immediately after starting the engine. My 2011 328 doesn't do this. Not sure if this is expected - I thought it is computer controlled and fan does not start until engine temperature reaches certain point. This was done early morning, so engine was cooled overnight.