According to an article in Ynet, a group of rabbonim, including Rav Shevach Rosenblatt and Rav Yitzchak Mordchai Rubin among others, have paskened that it is prohibited to have your temperature taken, whether manually or by an automatic system, on Shabbos, and therefore people should not go into hospitals or other public buildings on Shabbos (unless they are in a situation of pikuach nefesh). Hotels now are also problematic. According to the rabbonim, an acceptable solution would be for these places to have a non-Jew at the door taking the temperatures rather than a Jew or an automatic system. Having a goy taking the temperatures would solve the problem even to allow a visitor to visit a sick patient that is not in danger.

The problem with the temperature is both the electrical action of taking the temperature and also the "writing" on the screen when it outputs the temperature.

The rabbonim of the Tzomer Institute have developed a thermometer that they say is approved for Shabbos use. I do not understand why they felt the need to do so, considering that they argue on the premise and say it is ok to use digital thermometers on Shabbos because it is neither the act of writing on the screen nor is it an electrical problem because of the LCD.

Rav Reznikov, the rabbi of Ichilov Hospital, says using the thermal cameras that also take the person's temperature is no different than walking through the Old City of Jerusalem where security cameras record every step taken and every movement made. Rav Reznikov says the thermal cameras measuring temperature are even less of a concern than video cameras in the Old City or other places because the thermal scanners taking the temperature of people walking into the hospital are not recording that information anywhere, while the security cameras are recording everything.

Kipa brings the psak of Rav Meir Nehorai, the head of Beit Hillel, who says that the issue of the camera is not a problem as Rav Wosner paskened that the person himself is doing nothing but walking in. he is not taking his own temperature and is not doing any additional activity for that purpose. He also has no interest in the thermometer or temperature being taken. It is being done for the hospital's purpose, not his own.

Regarding the guard who is taking the temperature, it would be better if it would be a non-Jew, but even if it is a Jew, his job is to prevent a situation of pikuach nefesh that might affect the hospital and is allowed to take the temperature of people walking in. So, nobody is doing anything wrong.

Rav Nehorai also criticizes the psak prohibiting saying that such a general psak might cause people to avoid visiting the sick on Shabbos even when it is important.