Hi, during a cold-weather start up, you can start the aircraft APU at -40°C, ensuring that you have a minimum of 22 V for your APU showing on your DC electrical page. You can also start your engines at -40°C, when you do this, you will likely have a very high oil pressure during the start and obviously a low oil temperature. You do not want to increase the thrust until you have oil pressure in the green! The engine oil temperatures must be in the green for takeoff. There is a note for oil pressure that after cold start you might see 156 psi, 130 psi at idle for 10 minutes maximum. It also states that engines must remain at idle until oil pressure returns to within the normal range. Another cold-weather consideration is before the first flight of the day when the airplane is called soaked and an ambient temperature of -30 or below for more than eight hours, the engines must be motored for 60 seconds, and fan rotation (N1) must be verified, before the engine start is initiated. Thrust reversers must be actuated until deploy install cycles are less than five seconds.
So to summarize you can start if the temperature is -40°C, you must have 22 V or greater for the APU to start, once you start the engines, as mentioned you were going to have a high oil pressure, low oil temperature, You should not increase the Thrust of either engine and (remain at idle) until the oil pressure returns to normal. As far as takeoff, the oil pressure and the oil temperature all have to be in the green.
Hope that helps, Rob