You may be able to do it with a single stage non-inverting opamp; like
http://cq.cx/interface.pl#7 ,
but with a gain of 100 instead of 3.
The most important error terms will probably be the opamp's input offset voltage, and the device or resistor thermal noise. A chopper-stabilized opamp like the TC7652 has Vos less than +/- 5 uV, which is more than good enough. Noise may be dealt with by low-pass filtering the output, since the thermocouple signal is probably slow, tens of Hz at most.