I think the above gain seems to be an odd value.What about using those two gains?
Amp-A=100,Amp-B=5 ?? overall gain = 500.
So the outputs comes like this.
1'C=19.5mV
250'C=5.076V
Note:
*Don't worry on cold junction temperature (I don't care & I don't know what it is)
*Don't worry on accuracy issues I just need 1'C resolution.
*Limit to traditional Op Amps LM358,CA3140 etc....Do Not use AD595,MAX6675 etc........
*Also I have seen many commercial thermo controllers they used ordinary OP-amps.