In questions there may be discussion related to temperature. Some answers are using farenheit as the unit, others may use celcius.
What (if any) is the convention for usage of these units?
If you're really in doubt, list both. It takes about 3 seconds to type "10c to f" into Google and you have your conversion. Just make sure you mention which temperature gauge you're using - 60F is very very different to 60C. If someone elses question doesn't mention, but it's pretty obvious, then edit it in with a conversion to both F and C. Or to K as well if you really want to hammer the point home.
Really though this should go for anything where units differ between countries - for example, voltages. I received warnings once from a user who didn't realise my systems run on 240v - and why should he? I never made any mention of it in my question.
The correct set to use is the one you specify in your question. Unfortunately, due to the US dominance of the site, the unlabeled default is usually Fahrenheit. Except for when it isn't, such as that time of day when the US is sleeping and the rest of the English speaking world is active.
Which is to say, there is no canonical correct. Just be specific about what you're talking about, which will let people know that converting needs to be done.
While I agree with the simple "just state your system" notion, I have to mention that there is an international standard of measuring systems which is the official system to use in many countries (including most of the EU, with some exceptions for the UK and Ireland). I would consider it a worthwhile goal to get rid of the imperial system once and for all, so if in doubt, prefer SI units (adapted to use Celsius instead of Kelvin).
Depends! Since the site is most popular in the US, so F except in medical matters where it is C. In the metric world, it's C, except in medical matters where it is F (yeah, doctors like to try and obfuscate every little thing they do). Scientists typically use C or K
90 degrees F in C
into search. Do you really think this is big enough of a problem that we should attempt to educate and enforce this across the tens of thousands of users that visit here? Is googling the conversion is you can't estimate it in your head enough of a problem?