When medically necessary, one may use a regular mercury thermometer to take someone’s temperature. One may also use a manual blood pressure monitor. Although without a significant need one may not measure things on Shabbat, as this is a weekday activity, it is nevertheless permitted for a mitzva or medical need (SA 306:7 and 328:43; above 22:6). It is also permitted to shake down a thermometer so that the mercury contracts (SSK 40:2).
Some rule leniently and permit a sick person to use a thermometer strip, which displays body temperature upon being placed on one’s forehead’s. They maintain that this is not considered Kotev since the numbers are already imprinted on the strip, and the temperature merely makes them visible for a short time, after which they disappear (Yeĥaveh Da’at 4:29). Others maintain that using this type of thermometer is rabbinically prohibited, considering it temporary writing (SSK 40:2). Since it is a rabbinic law, one may be lenient in a case of necessity (Tzitz Eliezer 14:30; see Harĥavot 18:4:4).
The poskim disagree about whether one may perform a medical test on Shabbat that causes color to appear. Some prohibit this on account of Tzove’a. Others permit it, as one is not interested in the color, only in the test result. Le-khatĥila one should be stringent, but when necessary he may be lenient, since this is a case of uncertainty regarding rabbinic law (see SSK 33:20, and Harĥavot).