Isolation Amplifier? Reading differential voltage on 600 V lines
The high voltage AC (assuming..) common mode voltage on the thermocouple will cause problems for most signal conditioners. 

You can power the high side signal conditioner (maybe ADC too if you want) with a step-down transformer from 600VAC and a small power supply (won't be very cheap or very small), then use some form of isolation to get the signal down. I did this one time for 100kV using fiber. At 600V you may be able to get away with a commercial process signal isolator. Make sure the latter is rated for continuous operation with 600VAC and follow their instructions as to grounding etc.