The circuit shown in the figure uses stored energy in the multiplexer relay coil to boost the power-supply voltage from 3.3 to 5.1 V. This extra voltage enhances the amplifier's ability to produce a larger output voltage suitable for interfacing to a 5-V analog-to-digital converter. It also extends the measurement range of the thermocouple signal.
This technique requires the faster relays to be used in continuous switching mode for signal scanning at regular intervals. A switching frequency between 50 and 1000 Hz is needed so that continuous energy is pumped into the voltage-enhancer reservoir capacitor (C1) from the relay coil. Obviously, the circuit should not be used with very low scanning rates.
An OPA277 (www.ti.com) low-offset, low-drift op amp amplifies the signals from the type-K thermocouples. The 3.3-V relay is a 9852-3.3 from Coto Relay (www.cotorelay.com), and it's rated for about 100 million operations. An amplifier gain of 251 was used to get about 10-mV/8C output. The cold junction is to be read separately.