Newton's Law of Heating/Cooling

Hi. Here's another problem:

A thermometer reading 70 is placed in an oven preheated to a constant temp. Through a glass window in the oven door, an observer records that the oven reads 110 after .5 minutes, and 145 after 1 minute. How hot is the oven?

So I begin by listing the given information:

(1) $\displaystyle T(0)=70$

(2) $\displaystyle T(.5)=110$

(3) $\displaystyle T(1)=145$

A one parameter family of solutions to Newton's Law is $\displaystyle T(t)=ce^{kt}+T_m$ where $\displaystyle T_m$ is the constant temperature of the surroundings - in this case, the oven.

So, it seems like I would proceed by setting up and solving a system of three equations in three unknowns. Is this the correct method?