Am I filtering my LM35 signal correctly?

I measure temperature with an LM35 in an electrically heated water bath (temperatures up to 70°C).
It is plugged into A0 and gets GND and 5V from the Arduino. I use the internal 1.1V reference in the sketch.

When I had very short wires there were no problems, but as soon as I used longer (unshielded) wires, the readings started jumping up and down.
My first attempt of noise reduction, was to put a capacitor (47uF) from signal to GND before entering the Arduino. It worked like a charm, the noise was gone and the readings were reasonable. Unfortunately I’ve read elsewhere, that that is not the way to do it, because it risks overloading the output.

I then did as shown on the picture below using a 1k resistor and the 47uF capacitor.
It seems to work,the readings are stable, but seem to err on the high side, especially at higher temperatures.

Is this an OK way to reduce noise? Or do I risk overloading here also?

rc filter.jpg