it looks like the sensor can(?) accept a good deal of input voltage, some of the schematics mention 15v. Another thing, you are working with adc and need it to be compared to the supply voltage. I don’t know how PICAXE chips set that up, but, I would think it is worth looking in to to attempt to get good data from the temp sensor.
What value of resistor did you use for R1 (the resistor feeding the LM335)?
As birdmun has mentioned, you need to compare the voltage from the sensor to the ADC range to get the actual temperature. The value you are reading is 39/255 of the ADC range. According to the PICAXE manuals, the ‘readadc’ command uses 8bit precision - you can use ‘readadc10’ for 10bit precision instead, which will give you higher accuracy in reading the temperature.
Also from the PICAXE manuals: “Using the ‘readadc’ command does not automatically configure the pin as an analogue input. Pins must also be set as inputs (not outputs) for the analogue input to work correctly. The analogue voltage range can be the PICAXE power supply range or an alternate external voltage range.”