There'll be issues keeping that cool and the air fresh putting enough people into them. Also some of the most endangered places have huge populations that would make sinking enough shelters difficult. Depending on the soil composition that might be a short term solution too. The soil surrounding the London Underground is particularly bad for this and it's estimated that 80% of the heat ever generated in the Underground is still there in the walls.

https://www.youtube.com/watch?v=hQo6_GkITe0

If mankind has to start living at night because daytime is too hot, at least night owls will no longer have to shorten their life expectancy to fit into a daytime schedule.

Welcome to Spain.

I do wonder, if wet bulb temperature is a function of temperature and humidity (assuming reducing temperature requires electricity usually) will the real trick to reduce mortality will be to reduce relative humidity in a confined space. A supply of emergency desiccants somewhere at home may be an avenue worth exploring.

This was the original application of Air Conditioning: to reduce the humidity of air inside a building.

I suppose the best available option for a lot of people if designated shelters aren't available would just be to walk to the nearest body of water and climb in, and wade around until the heat subsides.

You're assuming the nearest body of water is somehow cool enough, which is often not the case.

Well, you'd have to take it on a case-by-case basis. I suppose as long as the water is at least somewhat below hot-tub temperatures it might be a reasonable way to sort-of cool off.

itd make more sense to lay a bunch of pipe underground and cycle air through it. or water in a closed circuit with a heat sink.

If you have power you can just use a heat pump like a window unit. This is about places with unreliable or negligible power grid.

Not practical on any Pacific island sitting just above sea level.

Sit in the water instead? The ocean water tends to be cooler than the air due to oceanic currents.

Excellent point. Woods not seen for interfering trees.