Chambord is a must. Without any doubt the largest and most famous castle in the Loire Valley.
The castle is so large you can almost get lost in there, the staircases are really cool!!
I was there in the middle of the summer and did not find it particularly cold.

Chenonceau is also a nice castle, indeed the one you see in many brochures promoting the region.
It's a castle that has a river flowing right under it so the castle actually works as a bridge as well. Interesting architecture!