Hi,
I need to know how can I test and identify if a MOSFET has failed or not due to high soldering temperatures. What can I do please, using just a simple multimeter? Thank you.

 

You should be able to read a diode junction from drain to source. The diode will be reversed biased in normal operation. All other terminals should check open.

Do the check on a FET in a known good board so you have some idea of what readings to expect. Checking in circuit is always less clear than out of circuit because of alternative current paths.