You want to limit your cycling to 5am to 9am and then 3pm to 6pm in the summer months.
Otherwise, stay in the shade in daylight hours and don’t move much. A six pack or two of taipi are optional but often warranted.
But from what I can see online, Yuli and Lishan average just under 30, which definitely make a difference. Rainy though, by the looks of it. Anyone happen to know if that’s all-day rain or just a daily shower/thunderstorm (typhoons apart)?
Lishan is pretty high up so it will be hot (but not humid) for a few hours and then well below 30 at night. Maybe even below 20 at times. My sense is that Lishan is partly affected by Yilan’s raininess but it’s hard to tell because mountain weather changes so quickly. It can be gorgeous up there.
That said, I would not stay in Lishan. It appears to me to be a dismal little high-altitude farming town with a fair number of dilapidated hotels left over from the days you could get up there from Taichung. It’s quite possible there are some nice corners hidden from the main roads as is often the case in Taiwan but they have eluded me.
Yuli like the northern 60% or so of the rift valley has a very distinct weather pattern of great weather in the morning followed by clouding over and a brief rain storm lasting an hour or two tops. You’ll need to be in the southern Taitung area to avoid this.
If you want to be in the mountains, try the Alishan area or Namasia in Kaohsiung. Dubang, Laiji, or Chashan in Alishan would be good choices. This minsu is Chashan is well situated and appointed for your purposes.
In Namasia, any of the towns on Highway 29 would work but I would choose Minquan simply because it would be the coolest. There is also Taoyuan over in the next river valley east.
Like Lidao (mentioned in previous post), these are all indigenous communities that have much more sensible layouts than Han mountain communities.
羅娜, 潭南, and 瑞岩 in various parts of Nantou are all similar.
Yuchi is a Han community just north of Sun Moon Lake that is pretty pleasant and more accessible than some other places. As I recall, it even has a supermarket.