That should work. It is not clear, however, what the input voltage range of the ADC is. You may have less than 10 bit resolution for your temperature range.
I would try it with the 5V source from the board. If it is too noisy or have drift you will need to provide a more stable supply. Try doing other things with the computer and see if the temperature reading fluctuates. Generally, computer power supplies (which this is) tend to be rather noisy when used for data acquisition. Since the board receives 5V from the USB port there is no headroom to regulate the 5V output on the board. There appears to be a regulator in the bottom left of the board, but it must be for a lower voltage used internally only. The LM34/35 temp sensors require at least 5V supply.
LM35 supports down to 4V. In my experience, these aren't that sensitive to Vs. Certainly nothing a cap or two couldn't handle. You could also average out any noisy readings in your code.
That's weird. I just now realized that LM35 can indeed go as low as 4V while LM34 needs 5V. I guess it has to do with the numerical difference of Fahrenheit vs. Celsius.
Your sketch looks OK. It is so simple it is hard to see what can go wrong. Well, there is one thing that still could be wrong, but you already checked the pinout. Do you understand that the pinout drawing is the view from the bottom of the sensor? If you think it is the top view then Vs+ and GND pins will indeed be reversed. Look at the data sheet again, compare to your part. That's the only thing I can think of now.
You are so right!!!
didn't notice the "bottom view" sign next to the drawing.
Getting much better results.
the voltage in the middle pin is 0.22v
adc readings 260-270 (doesn't make sense, the reference voltage is 2.5V)
vss 4.80-4.82