It uses a lot of components, but I think it fulfills your requirement. Or maybe it's not a lot - one diode, one resistor and 1/4 of an opamp package per thermistor.
This only works if the motherboard uses an ADC to measure the voltage. They often measure chip voltages, and the OP's circuit is capable of generating a voltage, so that's a reasonable supposition. However, it's still possible to measure that thermistor in other ways, perhaps charging and discharging a capacitor and measuring timing, which this circuit won't handle.
simulate this circuit – Schematic created using CircuitLab
Each thermistor generates a voltage with its corresponding resistor, reproducing the voltage that the motherboard expects to see.
Only the lowest voltage channel will control the output voltage through its diode. Opamp feedback removes the effect of the diode voltage drop, rather like it's used in a precision rectifier circuit. Thermistors generating a higher voltage will have their op-amp output at positive rail, with their diode reverse biassed.
You'll notice I've not specified the voltage rails for these opamps. If the thermistor voltage never drops below a volt or thereabouts, and you use a rail2rail or single supply opamp that can drive to close to its negative supply, then you will get away with powering it from GND as the negative rail. Diode leakage is not important in this circuit, so you could use schottky diodes instead of silicon to get down to 0.5 V output with a R2R opamp. Otherwise you'll need a negative supply. Positive rail needs to be at least Vref, or more depending on how high the output voltage is required to go.