I’ve been experimenting with my v60, EK43, refractometer and variable temperature kettle. I understand somewhat how grind size, water-to-Coffee ratio, agitation etc. affect extraction, but I am unclear on the role water temperature plays. I’ve heard 195-205 F is ideal slurry temperature, but how do I know when I might need to make a change in water temperature?
Agreed with the above answer by Jason: it's about taste.
That said, of late i have been surprised by how effective for extractin Scott Rao's 97degree C is for a pour over[link].In particular it seems that central and south american beans need the temp to get out the flavour - african's less so but still work in that range.
But to your question - a more specific mapping of flavours:
Matt Perger has a super chart to map when temp may come into play based on what you're tasting and how to tweak it. (2)
The best way to detect what's happening is with your tongue. Try doing two batches brewed all the same minus temperature. Start out at 190 vs 210 and close in until you can't tell a difference. Use various palate cleansers (like cereal or eggs and switch between sweet/salty/sour foods to really get a picture of what's different between the two batches). Taste the coffees at various temperatures, sometimes coffee can get sweeter when it's cooler. Try out the coffee cupping tasting slurp method.
Refractometer might tell you a gravity reading, but it doesn't tell you anything about flavor or mouthfeel. Finally go with what tastes the best, and realize that for any particular grind size, brewing method, and coffee combination, the perfect temperature of your water will vary.