Precise multi-point over-temperature control using comparator
As the LM339 has open-collector outputs, you can scrub the output gate and wire the comparator outputs together in a wired-OR fashion.
You will only need a single pull-up on the output node.
As Tony commented correctly, you should double check your threshold polarities. The wired-or demands that fault cases lead to (active-)low comparator outputs.
If any circuit detects an Over-temperature, the respective comparator will pull the whole output down. The output only pulls up, if none of the comparators are in the active-low state.