One of the two digit 7segment display will read its values from a smoke sensor while the other will read its values from a temperature sensor. From what I have seen in textbooks recently;each segment display will make use of ten digital pins(7 segments, decimal point, display faces(correct me if I'm wrong Pls)).
You are correct about the 10 pins, shift register are probably the way to go for you. They are very cheap and pretty simple to use. Try googling 74hc595. It basicly turns 3 pins into 8, and you can even Daisy chain the chips to get 16, 24, 32 and so on from the 3 pins on the arduino. Good luck to you.