Delay won't help, the sample/hold capacitor is isolated at that point, it gets connected to the input multiplexer for 12us before each conversion.
Normally there should not be any problem if the input impedance is 10k or less as the sample and hold cap will charge fully in that 12us.
The LM35 has low output impedance though... Try putting a 10nF or 100nF to ground from A3, that ought to eliminate noise and stiffen up the voltage there. The long unshielded cable to the sensor is going to be picking a lot of noise from the computer.