I am using a stand alone XH-W1601 PID controller but I would like now to record the temperature readings, not just display them.
I am not sure how to do this, maybe just measure voltage as analog signal in the T sensor input? or will that disturb the signal?
Rather than trying to understand how that device works, and most likely failing, a much better approach is to buy a DS18B20 temperature sensor and connect it directly to an Arduino. Plenty of reliable software is available and the total effort will require just a few minutes of your time.
You can save data on an SD card, or send it out the serial port to a laptop.