How to solve system of two or three differential equations

Hi, I am solving heat balance between 2 and 3 offices. According to that, I define following equations:

C1*diff(T1(t),t)=U*A1*(T1(t)-T2(t)+U*A2*(T1(t)-T3(t))+H1(t); C2*diff(T2(t),t)=U*A1*(T2(t)-T1(t)+U*A2*(T2(t)-T3(t))+H2(t)

I want to analyze change of temperatures in both offices over time, also in case that heater is turned off in one room, etc. Furthermore, I want to set up thermostat control because of overheating in the room.

One more thing, I want to solve this system in discrete time, so I hope that somebody could help me with solving.