Yes, if Vcc is 3V3 then ADC input max. value is also 3V3. So for the calculation it would be 3V3/1024 * analogRead / 10.
For your example the two values in the I/O sample packet are 0x53 (MSB) and 0x00 (LSB) which is 83 in decimal.
(3V3/1024) * 83 = 0,2674 V = 267,4 mV / 10 = 26,74°C. That value might be ok if your room temperature is that high
According to the datasheet the LM35DZ operates from 4 to 30 volts. 3V3 is less than that - maybe that's the problem, if you get any wrong values.
How did you measure the 0.31V output? Was Vcc > 4 volts?
If you need a temperature sensor which works with 3V3, then try TMP36.