Hi

Throw away the crazy 4051 ,it is not suitable for industerial sites,I suggest you fault resistance ADG506/7/8/9 multiplexers for THC multiplexing(use industerial versions)
see analog device site ,They have application note on THC multiplexing with AD594/5

you do not need amplifier,use direct sensor to digital ICs like as sigma delta ADC converters like as analog device AD77XX seried(AD7714,15,19)

for cold junction comp. use NTC(precision types or temp ICs and use software compensation and linearization.

at now this info is sufficient for you!
bye