So if my summer water temp go out to high I have created and indoor tank
that's big enough for about 15-20 trout. Just in case. So I can just take them out when its too hot and throw them back out in the fall.

That'll work! Get a filter system on it, and have a way to remove excess food and poop.

So its 8x4x4 how many trout can i fit in there safely in the 9-10 inch range

A cage 8x4x4 is 128 cu ft and easily 1 trout per cuft assuming cage mesh size of 3/4" to 1.25". Fewer trout would be okay since trout are not very territorial in a cage. Smaller the mesh size the less water flow. Trout need good water flow through cage to maintain higher DO concentrations and flush out waste products. With good water flow through cage and cool water less than 65F one could put at least 3-4, 9"-10" trout per cuft. As a rule fewer trout of 1 per cuft should be used when larger fish are used and mesh size is smaller than 3/4". Watch the fish often and closely as water temp gets above 60F. When they quit feeding they are in TROUBLE!!!

So brown brook or bow? Oooo what about golden!!!

Will trout thrive in an indoor setup?

I don't see why not as long as you keep the water clean, cold-55 to 60, and plenty of O2.

I know if trout aren't happy they get stressed and die. Thanks and I will post some pics