I think most of the model creators share their model usage examples so high at 0.6-0.7 simply because it's what a lot of the client apps use. IMO this is WAY too high unless you're doing creative writing.

Generally I set temp to 0-0.4 at absolute most.

min_p actually needs a little temperature to work effectively so with min_p I almost always use 0.2

Ye lower temp is also good :) Tbh its all trial and error - I found temp=1.5, min_p=0.1 to be very useful for pass@k type workloads - ie calling the LLM multiple times and aggregating.

temp=0 is also good for singular outputs. For classification tasks, it's better to actually inspect the logits.

But my goto setting is always setting min_p at least 0.01 or 0.05! It vastly suppresses incorrect rare random tokens from being created, and it helps massively!