Hallo Abhishek,

normally, LM335 can be handled very easily. Because of it's low impedance (it's a zenerdiode!) hum and noise does not present any problem in most cases. Use of unshielded twisted pair with standard RC low pass filter at input of amplifier will suffice in most cases.
If hum suppression is of interest, corner frequency of low pass filter should be much lower than 50Hz. With bipolar OPamp 10kOhm plus 2.2µF (mylar) is a good choice, for FET OPamp 1MOhm plus 100nF (X7R) can be used.

I would suggest an operational current of >=1mA, but as close to 1mA as possible. So, with +15V power supply simple 11kOm resistor will act as trivial 'constant' current source.

When interference is very high, use of shielded twisted pair can be of help. Connect shield directly at input of amplifier to signal ground. Shield should be extended over LM335, if possible. This would form a Faraday cage, which shows best shielding performance.

Anyway how LM335 is mounted, low thermal resistance between case of LM335 and object (which temperature is to be measured) must be provided. When not using any shield or additional enclosure and LM335 is in direct contact to object, no problem arises. But if LM335 has no direct contact, because there is an additional media between (enclosure e.g.), thermal contact between case of LM335 and media should be improved by the use of thermal grease or special 2-component epoxy glue providing low thermal resistance.

If no low thermal resistance between case of LM335 and object exists, self heating of LM335 can present a problem. It's not that self heating will overheat LM335, but result of measurement will become eroneous.
If 1mA is flowing through LM335 at 3.75V output voltage (Tj=100°C), power dissipation is only 3.8mW. This is maximum heat dissipation with +15V supply and 11kOhm resistor. In combination with 200°C/W thermal resistance between junction and ambient (TO92 case), self heating will introduce an error of 3.8mW x 200°C/W = 0.8°C. At room temperature error will be about 0.65°C.

In case of air temperature merasurement error can be minimized, if case of LM335 is brought into close contact (special epoxy glue) to some material, which has the same temperature as air and which has lower thermal resistance to it. Then, bit lower 170°C/W thermal resistance between junction and case comes into play, which presents a slight improvement.
If on the other hand, LM335 sits inside an enclosure or shield, with case of LM335 having NO good thermal contact to it, 200°C/W thermal resistance between junction and ambient is no longer valid, because then heat transfer to ambient is highly worsened! Then, use of special epoxy glue can result in dramatical improvement.

Now to your second question: What, when mounting LM335 to a heatsink?

From above calculation it can be seen, that with 1mA operational current junction temperature rises to not more than 1K beyond case temperature. Keeping in mind, that maximum operating junction temperatur for LM335 is 100°C, it follows, that heatsink temperature must not be higher than 100°C!

Kai