Thermocouple + Instrumentation amplifier. Does it make sense to have one input grounded?
If you are reading a thermocouple, it might be reverse wired so as to produce a negative voltage rather than a positive voltage that could be resolved by a single-rail op-amp.

I would still use an InAmp (because of this) and I would ensure that it operates on +/- 5 volt rails to provide sufficient headroom to avoid input common-mode range issues.