Let's say I have:

1: one mole of extremely cold ideal gas  

2: unlimited amount of ideal gas at temperature 300 K  

3: one ideal heat engine

Can I generate for example 1 MWh of mechanical energy using those three things? 

Alternative formulation: When temperature of the cold gas approaches 0 K, what does the amount of generated energy approach?

(there is no other heat sink than one mole of cold ideal gas)