Is it safe that my medium-rare steak is cold in the middle?
Solid meat (such as a roast or steak) can be quite rare on the inside and still be considered safe by conservative government or academic standards. Solid meat is different from ground meat because bacteria (Salmonella and E. coli are of particular concern) get mixed into the meat from the surface when the meat is ground. When you sear a steak, you effectively clean the surface where the potential bacteria live.

Those same conservative standards don't recognize rare (as in cold) as safe. However, steak tartare and other raw beef is served in restaurants all over the world. 

Source Academy of Nutrition and Dietetics

According to the same extremely conservative source:


  the meat needs to reach 145°F internally and stand for three or more minutes before cutting or consuming. Unfortunately, even if preferred by foodies, there's no way to guarantee the safety of rare meat. That also means raw meat delights, like steak tartare or beef carpaccio, are not considered safe.


I have many years of experience eating very rare and sometimes raw beef. If the  meat is fresh and from a reliable source, I have no problem eating it very rare.

The standard caveat applies that extra care (and heat) is required for the immunocompromised or pregnant.