Castle isn't going to delve into deep questions about the ethics of cryogenics, but it can have lots of fun with the frozen head. With this premise, "Head Case" is solid episode with some snappy dialogue about the subject. The conclusion of the episode was better and more sobering than usual, as the wife had killed her dying husband so he could be frozen and later killed herself in the jail cell.
It was a little surprising that Alexis didn't actually get into Stanford. Television high schoolers always seem to get into the best colleges without studying or taking hard courses (and the occasional AP class obviously would not be enough in the real world). Alexis is unhappy but Castle saves the day as always.