If your compost pile gets hot, then the worms will get cooked. Not good.

That sounds just like my first batch of worms- They hated me!!

I think you will be OK putting them in your basement. If you have a rubbermaid set up, and your holes are too large, just set your first tote (with the big holes and the bedding) into another identical tote without any holes. Leave the lid off both totes, and the light on in the basement, right above the totes. Don't turn off the light. The worms like to explore a new place in the dark, and don't realize that the tote is home yet. Just tell your care taker to leave the lid off and the light on, and as long as the tote is damp, not wet, and has some bedding, they should be fine.

It appears to be normal for some exodus on new setups.
My first batch in my basement I lost quite a few that crawled out and died. I left the light on a few days till they got used to the rubbermaid.
I started another bin and they also ran on the floor so I had to leave the light on for a few days also.
I now call the area of my floor , the "Trail of Tears" for all the worms who didnt make it. :)

I cannot build a compost pile without having worms show up and take over when it cools off. I usually add aged horse manure in my compost with worms and cocoons already present. When the pile heats up the worms head toward the sides and down. After about 3 turnings the pile cools and I get a bloom of surviving cocoons hatching. I add a couple pounds of worms to it, cover with burlap or old carpet, and keep moist. Let the worms finish your compost!

Thanks so much everyone