On the one I owned briefly, temps less than about 80 degrees, I could see changes in one step. As the temp pushed into the mid 80s, the tuning knob made less and less difference, and past about 85, the filter would not tune. The green light would never come on and while I could usually see some bright prominences, little surface detail could be seen.
I think the response to temperature of different Quarks can vary a great deal. I have read other accounts where people say that they would not get a green light in some conditions and when that happens, the tuning becomes insensitive because this seems to indicate that the unit is too hot. Turning the knob may not seem to make much difference when this happens.
And this isn't me just yaking. If you read the Quark Manual, it clearly says this but it is talking about the inability to get solid green light which means that the temperature is not being regulated properly. This is a direct quote from the Troubleshooting section of the owner's guide. Emphasis is mine,
If after 20 minutes of the same knob position setting the LED has
not turned green, the ambient temperature may be too hot or too cold for
the Quark to regulate the temperature. However, the filter may still be
usable while slightly mistuned and performance may not be affected.
Now Daystar says that the Quark performance "may not be affected" but that is marketing talk not having to say the performance can be affected.
So, yes, heat can affect tuning behavior on the Quark and at over about 85 degrees, mine simply stopped tuning surface detail though I could still see proms if I moved them to the edge of the field of the quark.
Once again, this seems to vary by individual Quark. Many report no issues at all, some report that they no longer get a full green light but the Quark is still usable, and apparently some just stop tuning and you get whatever band with it leaves you with, and no amount of turning the knob will improve the view.
If you are getting a solid green light though, this likely would not be the issue. If you are getting a partial green, then suspect that the Quark is no longer capable of regulating the temperature.
And now people will rush to defend the Quark, but that has nothing to do with your questions. You asked if temperature mattered, and the answer that in some Quarks it might matter a great deal but in others, maybe not. I used Daystar words above, so I am not making anything up here. The Quark can be sensitive to heat and cold and the manufacturer very un-clearly states that to be the case.