Multiplex temperature signals through one conditioning circuit
Multiplexing a single conditioning circuit for use among multiple sensors is a common method to minimize the amount of hardware required.
Temperatures tend to be very slowly changing so cycle times of many seconds is usually acceptable. This allows many sensors to share the hardware.
However, some caution is required to ensure that the multiplexing does not corrupt the incoming signal from the sensor.
Many systems use thermocouples as the sensor but one characteristic of them is that they only produce very small voltages, a few microvolts per degree. So you need a multiplexer that can switch such small voltages wihout significant errors.
Mechanical relays are a common way of doing the switching, often reed relays. They can switch in a few milliseconds and have low voltage offsets. Semiconductor analog switches can also are often used, providing their higher on-resistance is accounted for.
Resistive sensors such as RTDs or thermistors can also be multiplexed although the excitation for those may also have to be switched.