Hallo Abhishek,

I would try to put it inside of PC. I think that noise is no problem, as long as sensors are delivering quasi DC signal and you can put low-pass-filters with corner frequency of much lower than 50/60Hz at input of temp sensor amplifier.
Again it would be the best to have Faraday cage of PC extended over temp sensor circuitry. This would need the use of shielded cables. Shield should be connected to backpanel of PC.
Then you can go two ways: Amplifying temp sensor signals by a symmetrical amplifier, which would be best but expensiviest, or to use simple unsymmetrical amplifier, where the one contact of temp sensor is connected to 0V of PC card and the other is considered of carrying signal.
If temp sensor at measuring point sees no ground or earth connection, so when it is isolated from cable shield at this side you will not suffer from ground loop hum or noise.
I would use a RF-filter at the point where cable goes into PC enclosure, and an additional low-pass-filter directly at input of amplifier. The first helps you to be compliant with EMC rules, the second eases PCB layout, you now, electronics on your PC card may produce some noise on it's own ground routing.
RF-filter can be just one capacitor to ground of input connector, it depends on your need. Second filter can consist of a rather large resistor (in combination with high ohmic impedance at sensor signal amplifier) and a rather large capacitor.When using 100kOhm and 1µF a corner freqquency of 1.6Hz can be achieved, resulting in dampening of 50Hz hum of 30dB or in other words a reduction of 97%. So, in most cases you will not need a symmtrecial amplifier.

Bye,
Kai