Concretely spoken, there are three ends and three thermocouples. Assume that the thermocouple sensor consists of two wires A and B, which are connected together at one point. This point is brought in contact to the medium to be measured and is at temperature Tm. At the other end these wires are connected to the electronics. Here both wires A and B must see exactly the same type of metal, let's call it C, and these two contacts must be at exactly the same temperature (Te). So, what you finally measure is the sum of the EMKs of three thermocouples, Te x (Uc-Ua) + Tm x (Ua-Ub) + Te x (Ub-Uc) = Tm x (Ua-Ub) - Te x (Ua-Ub).
Take note, that metal C plays no role finally. It's only purpose is to bring wires A and B at the far end on the same temperature.

Te is the temperature of the electronics, which is varying of course and affecting the temperature measurement of medium. If you had Te at 0°C, then you could easily determine Tm from the measured voltage. But as Te is higher than 0°C at room temperature you get a smaller signal voltage, because the temperature difference is smaller. So, you need to measure Te and to add the term Te x (Ua-Ub) to the above sum to get the correct temperature of media, Tm, in °C.

Kai