Chief Rabbi of Israel Rav Yitzchak Yosef has added his voice to the discussion and piskei halacha regarding entering a hospital, or other public building, on Shabbos at this time when temperature will be taken either automatically or via the guard at the door.

According to the report on Srugim, Rav Yitzchak Yosef has paskened that people need not worry and can go into a hospital that has a system of thermal cameras checking temperatures automatically of everyone who walks in as a safeguard for public health.

Rav Yosef differentiates between automatic systems and someone manually checking. His allowance is ONLY for automatic systems checking people's temperature. If a non-Jew is at the door checking temperatures of people entering, one could enter if there is a need for a sick person even with no life-threatening danger involved, such as to visit the sick or a sick person who needs to enter.

Rav Yosef compares this to the allowance to walk in areas with security cameras taking video surveillance. The person walking has the status of "pski reisha dlo neecha lei" - an act is going to happen because of him but has absolutely no interest in it and gets no direct benefit from it. So the video cameras are allowed when happening automatically, and so is the automatic thermometer taking temperatures.

The one thing missing from the article is regarding the situation of a Jewish guard at the door taking temperatures manually. The other rabbonim I mentioned in the post last week did discuss such situations as well, but Rav Yitzchak Yosef does not. Perhaps it is not relevant as all hospitals use gentiles? I don't know, but it seems to be an important point that is missing.