The straight answer is on web sites that provide weather info from data supplied by government sources such as the National Weather Service. Here's one such site that I use frequently and have found reasonably consistent with my actual experience.

http://www.weatherbase.com/

Weather info from posters on these boards is usually anecdotal and not to be relied upon. (Although it might accidentally be right.)

many areas of Idaho will be very hot in August

Going to depend largely on the elevation, with mountain areas pleasant and Snake River area much warmer, even hot. What part of the state are you planning on visiting? Northern Idaho isn't too bad and there are some nice lakes to recreate on up there as well.

I don't deal well with very hot weather.

How hot is "very hot" to you?

We thought we would fly into Spokane, visit the Coeur d'Alene area and then slowly make our way south through Hell's Canyon down to Boise, Twin Falls, Craters of the Moon, Sun Valley and then head to San Francisco. I'll travel around with temperatures in the 80s but if it is going to be in the 90s every day (other than up in the mountains), I won't be comfortable. I guess part of my question is which areas of the state can we expect this hotter weather (where is the Snake River area you refer to) and which areas are considered the mountain areas and will be cooler.

Thanks so much for all your help.

I was in central Idaho (Stanley and Challis) last August. At least in Challis it was pretty warm (?low 90's) during the day, but very little humidity so I tolerated it easily (I don't like heat either, and this was an outdoor event). At night it was delightfully cool. The Stanley area is at a higher elevation and cooler--perhaps low 80's during the day. It's a beautiful state--you'll love it.

Coeur d'Alene area and Sun Valley should be OK in August, Twin Falls and Craters of the Moon somewhat warmer. I'd follow dbdurand's advice and check temps on these half-dozen or so places you mention.

where is the Snake River area you refer to

Snake River runs east-west in the bottom third of the state thru Idaho Falls, Twin Falls, a bit south of Boise, roughly paralleling the freeway. Nice in the eastern part of the state in the forest, where it's high, but gets warmer as you go west and drop elevation.

Thank you all so much. I think we might save Idaho for a time when we can come in September and not have to worry too much about the heat. We're thinking of British Columbia for next August instead. I thank you all for the very prompt and very helpful information.

Since you have more than 15 days to work with, why not fly to Seattle (probably cheaper)and rent a car to visit Vancouver. After seeing British Columbia, head east to Banff, Alberta. From Banff go through Calgary and Cardston to St. Mary Montana. From St. Mary go over the Going to the Sun Road through Glacier NP. After you get to Whitefish you can decide which part of Idaho you want to see. Either South on US 93 or West on US Route 2. If you don't spent too much time in one place, you should get to SF in time for the wedding. I hope it is not too hot there.
Seattle is a good 2 day drive from San Francisco to turn in the rental car. Don't forget your passports to visit Canada.
There are plenty of cool places to see in Oregon as well.

I would suggest BC to be a much better option for you than Idaho, particularly if you've never been to either.

BC is little short of amazing, and at 133% the size of Texas, there is always plenty to do in the climate of your choosing there.

I went to Idaho in late July a couple of years ago, and in Lewiston it was 107 after 6:00pm. Missoula, MT (very near to the east edge of the Idaho panhandle) was 104 two or three days in a row. If you "can handle 80's" but not 90's... then you should probably visit BC instead. Though I should mention that Idaho doesn't have much humidity relative to points east and south in the USA.