When one opens a refrigerator door, there are two classes of effects:
Immediate result - e.g. light going on, or in newer models a fan might start.
This class of effects can normally be fairly easily circumvented on shabbat by removing the light-bulb and/or ensuring the sensor which checks whether or not the door is closed is continually activated for the whole of shabbat (e.g. by using tape or magnets).
Eventual response - opening the door allows warm air to enter, which will affect the refrigerator's thermostat, and, eventually, trigger the motor to cool down the refrigerator.
In this article from Machon Zomet, they write that their approach is not to worry about this second class of effects, because many poskim, most prominently R. Shlomo Zalman Auerbach, were not concerned about the indirect effect on the thermostat.
However, they note at the end of the article that there do exist refrigerators with a 'mehadrin shabbat mode', whose purpose is to neutralize the effect of opening the door on the thermostat, and that they define the use of such models as a chumrah.
With whose opinion are these 'mehadrin' refrigerators attempting to comply?
Please cite sources from Rabbis or poskim who either forbid or discourage opening a refrigerator door due to the affect on the thermostat.