...Here is a link to a figure showing the amount of time that it takes to decrease the population of a certain type of bacterial spores by 90% at different temperatures for both wet and dry conditions. ... As such, its really hard for me to see how using heat to try and eliminate or control a dangerous bacterial outbreak onboard a ship could be used to solve the problem.
I talk about one or two thousand two degrees, you post a link about 170 degrees? You do understand that the temperatures NIH is talking about are lower than some cooking temperatures, yes? Chicken, for example, gets cooked at 176 C for about an hour or so. No, the temps we're thinking about would reduce chicken to carbon soot in short order. That's the point: use temperatures that organic chemical bonds cannot survive, and the organisms on which they are based will - well, be reduced to carbon soot. It's about bond energy: pump in enough heat, chemical bonds break. Nothing made of molecules can survive that.
As for cooling - if you can deal with the heat of a fusion plant (which is most likely giving you the heat you need for the sterilization in the first place), then chilling a sterilized gas is child's play. In fact, there's a very good chance that heat is the method you're using to break down CO2 to get the oxygen free, since you've got all that free heat available in the first place, so you're very likely killing two birds with one stone. After that, it's just a question of capturing the carbon.
...The alternative though would appear to be to leave everyone in the same confined space of the main ship with people already know to be sick and in a contagious state. ...
Here's an interesting fact. If you're in a nursing home, and you come down with a highly infectious airborne disease, you know what they do? They make you stay in your room. You don't go to a hospital unless you actually need hospital services to survive. The only protection for the other residents is the door on your room. The staff wear masks, gowns and gloves when they enter, they remove that garb as they exit and deposit it in a red plastic garbage bag clearly labeled with a big biohazard label, in a big red trash can similarly labeled; the bag gets picked up by a company specializing in biohazardous wastes, and the bag gets incinerated. Housekeeping staff, wearing the same gear, clean the room daily with chemicals identified as deadly to the organism. CDC calls it "airborne isolation precautions".
Chlorine bleach in sufficient concentration is wickedly deadly to organic life, but there are other chemicals in use as well 'cause a lot of folk find the chlorine concentration hard on the nose. However, if all else fails, chlorine bleach in sufficient concentration will kill anything that depends on organic chemical processes.
Also pretty deadly, interestingly enough, is oxygen; ozone (O3) can be more effective than chlorine, and a pure O2 environment is deadly to bacteria (and hard on humans for a variety of reasons). However, a pure O2 atmosphere represents a significant fire hazard - things that are ordinarily only mildly combustible will burn like gasoline in a pure O2 atmosphere.
Also very effective is ultraviolet light; burns the buggies worse than it burns you, 'cause they don't have pigmented skin to protect them.
And, as we mentioned, high temperatures.
The ultrahigh protective measures used against certain extreme diseases reflects their lethality more than anything else. Interestingly enough, the typical Traveller vac suit offers more protection than the best modern biohazard gear, 'cause Traveller vac suits are reasonably resistant to puncture. So, the best defense in an absolute worst this-little-airborne-virus-has-wings-and-homes-in-on-warm-bodies-at-a-range-of-20-meters case is still to get your passengers into rescue balls and your crew into vac suits to stop transmission dead in its tracks - after which you wait for further direction from the infection control office of the port authority, 'cause if you try to land or leave a ship with that kind of infection aboard, the best way to sterilize it is to put the ship and anything leaving it at the heart of a nuclear explosion.

......if you are on a ship and someone has come down with an infectious disease that may have (or even may be threatening to) spread into the main ship's life support systems ...
I think we've established that the life support system is not at risk of harboring infectious disease - at least not for long. Between intakes and the output vents is a space that is deadly for microorganisms, so the cycle of spread is blocked. As for any organism that manages to hide short of that deadly space - say a bacterial strain lodges in an outlet vent while the system is idle for some reason - a pure oxygen flush will kill them. Or build the ductwork with internal UV emitters.
The thing to remember is that these are life forms. Even the most wicked bacteria are vulnerable to the basic things that rip up molecules, because they're living things that depend on molecular interactions to survive. Viruses are less vulnerable since they're essentially inert until they find their target, but they are still vulnerable: bust up their molecular construction with enough heat or the proper disinfectant, and they ain't viruses no more. It doesn't matter how alien the little thingie is, it still has to obey basic laws of chemistry.