So if medium rare is 145 degrees, you set it to 145, stick it in the oven and when it beeps you are done and its ready to eat? That sounds like the basic way of working a thermometer.
On a side note: Ppl tend to leave it wrapped up for a bit before eating (so ud set the thermometer for like 140ish?). Also - for a shabbes lunch meal it must be tricky as u need to warm it for several hours on Shabbes day as well.
NOOOO
Medium Rare is not 145 - ignore the FDA. use this chart
http://amazingribs.com/tips_and_technique/meat_temperature_guide.html.
As an aside, there is lots of great meat science on the website.
I like my meat rare to med rare, so I usually take it out at about 118 and find it always goes up to about 128-130. Shabbos lunch would be tricky, but my wifes family makes rare meat all the time. But you can't heat it it up or it will cook fully. They leave it out for an hour or so, so it's not like ice, and it's really good.