The pins are not tri-state as you wrote about tri-state.
A pin can be output with strong (40mA) 0V or 5V.
A pin can be input, which is a very high impedance input. An internal pullup resistor can be added.
But when the UART is turned on, it takes over the pins and sets the TX to output and RX to input.
Are the 12 units also Arduino boards (or Arduino compatible) ?
So you can program the units and the central unit with whatever you want ?
You could chain-link the serial communication, but if one unit fails, also the rest looses the communication.
For a wired-or/and you can use logic gates, but also 12 diodes with a pullup resistor.
The collision detection could be a problem with 12 units. What if they resend with the same timing ?
It is better if the central unit polls the units one by one. The central unit TX is connected to all the RX and the central sends "0t" to request the temperature of unit 0. When you add a timeout, you can detect a missing unit.