Do I need to upgrade my alternator with these fans?

The alternator doesn't have to match the instantaneous loads. The battery can do that. The alternator's job is to keep the battery charged, so if it isn't running down over a week of driving, you have no problem. Put the battery on a charger every Saturday. If it shows "fully charged" in <30 min, your alternator is keeping up. The electric fans should only run when idling for a long time.

You also need to "calibrate" your dash temperature gage. There should be a "normal position" which indicates where the thermostat is controlling. That will vary +/-10 F, depending on the heat load, since it takes a higher temp to open the T-stat more, but once fully open temp will go up quicker with load. If you know your T-stat's setpoint, that calibrates your gage. It sounds like it might be 180 F and your gage agrees.