The molecules in molten silica tend to form chains and even three-dimensional structures, depending on their impurities and temperatures. This is the main reason why molten silica is unusually viscous. Most other molten rocks consist largely of compounds that either do not much form chains, or include small molecules that act as lubricants between large molecules that otherwise might have tangled, resisting flow and increasing viscosity. It is possible in principle to heat silica to near its boiling point, where its viscosity is greatly reduced, but that requires temperatures of about 2000°C, which is far higher than typical temperatures in the Earth's crust. Molten silica and silica-rich melts underground generally are very viscous and commonly contain a fair amount of dissolved carbon dioxide or water, which might reduce its viscosity somewhat but are responsible for explosive positive feedback when containment of the pressure fails. While it certainly is true that hotter, less viscous silica is more inclined to mix, it does not follow that a large body of viscous molten rock will mingle easily with anything else unless there are considerable kneading forces. We are after all not speaking of turbulent flow in most cases, so the concept of stirring rather than kneading hardly applies. In practice effective mixing usually happens mainly near the interface between different types of molten rock.

The question: "…is magma viscosity really more influenced by temperature which effectively controls the silica content? rather than just the physical properties of silica making things viscous?" implies its own answer to my mind. It depends on the circumstances. Under volcanic conditions silica is a viscous substance and its viscosity is influenced by both its temperature and its impurities and solutes. An atypically pure silica will be highly viscous at modest temperatures and dramatically more fluid only at very high temperatures. Magma with a low silica content will generally be fluid down to quite modest temperatures. Although viscosity does influence the ease with which magma components mix, I would have strong reservations about accepting that temperature "effectively controls the silica content". That strikes me as an unjustified overstatement unless you can specify the circumstances in question, and support the suggestion that such circumstances are relevant in the behaviour of explosive volcanoes.

I think my discomfort with your question is that you seem to be asking for a notionally quantitative answer to a qualitative question. It is not the sort of thing that one can sensibly answer without quantitative experiment in response to adequately formulated conditions.