How can I estimate the time required to bring a piece of meat to a certain temperature?
I think this will be impossible to do accurately, in an oven, without a thermometer. I know you want to estimate, but a few degrees will be the difference between rare and medium rare, for example. Variables include: thickness of steak, internal temperature of steak when you begin, accuracy of your oven temperature, and time.  In an oven, even though you set the temp for 275...not only might that be inaccurate (thus the use of oven thermometers), it also fluctuates fairly widely throughout the cook time.  

If you were cooking in a water bath (sous vide) you could solve this problem with excellent accuracy.  See http://www.douglasbaldwin.com/sous-vide.html#Beef

Caution: Do not apply Baldwin's charts to oven cooking.