As a former boss used to say, there is no "fairly sterile" just as there is no "fairly pregnant".
This (and mrob's post) is definitely incorrect. It's the opposite, in fact, there is no "sterile" in the absolute sense. You'll never kill everything.
This is measured in multiple ways, depending on field: sterility assurance level[0] is one, similar to the way the USDA specifies cooking temperatures to hit 6- or 7-log reduction in bacteria populations. This is also why we crash probes like Cassini into Saturn to not risk contaminating any possible niches that could support life even though the probes have been built in a clean room, cleaned, and irradiated.
I suspect that there's some level of heat at which you've done exactly that. What organic molecule is going to survive a bath in liquid tungsten? ~6100F
There's also flaws in procedure -- was it at the required temperature long enough -- and, of course, the real world that your target is going to be exposed to when it leaves the tungsten bath -- clean rooms aren't all that clean.