Directly under the sensor on your dash there should be another tube - it comes down from that sensor.

The way the whole tube thing is supposed to work is the actual temperature sensor sits inside the little black grill on your dash. The tube going back to the firewall leads to the input side of the blower fan. The fan causes air to be drawn in through the grill in your dash and across the temperature sensor, then into the fan blower. It improves the accuracy of the temperature sensor and makes the climate control system more accurate. It isn't required for your system to work, but without air pulling across the sensor it'll just be reacting to the dash temperature, instead of the air temperature in the cabin of your car.

The actual sensor is just a tiny little thing that looks like a soldered wire end. You should be able to see it through the grill in your dash. I'd take pictures of all this to show you but my car is currently in a shop 40 miles away getting a rebuilt transmission.