Shielding a long cable
For a remote passive or a device that is solely powered down the cable, the shield should be tied to ground where it has most impact on preventing noise getting into sensitive input circuits. The noise comes from the long length of cable and the shield/screen acts like a faraday cage to this noise and grounding this faraday cage right at the receiving end i.e. at the input receiving stage takes all this noise to ground. This is the best place but there are exceptions.

If you grounded the shield elsewhere (such as at the sending end) and left it unterminated at the receiving end you will get a noisy signal into your input circuit. Of course the dilemma occurs when your remote device is earthed. See this below: -



To avoid ground currents from other pieces of equipment contaminating the cable with unwanted earth currents you should use the capacitor at the receiving end - this attempts to minimize low frequency AC power currents circulating through the cable whilst giving a decent protection against RF induced noise.

Taken from here - Analog devices MT-095, EMI, RFI, and Shielding Concepts.

Regards the LM35's ability to drive into capacitors (coax cable or normal capacitors), there is a range of capacitance where the device will become unstable so you can either feed the output into a cable via a series resistor or shunt the output with a much larger capacitor in series with a resistor. In fact most op-amps exhibit this behaviour.