What is the connection between an actual crucible and the crucible book?

I think there are multiple connections there. Cauldron (as in witches) is a kind of crucible. And a crucible is a place of heat and turmoil as it boils. Miller was prompted by the McCarthy UnAmerican Activities Committee inquiries, and no doubt some of those the focused on felt like they were being boiled alive. And it might have just had enough feel and vague sort of feeling to sound right. Of course, it might also be Miller making a little joke about his play. A "potboiler" is a somewhat poor play, a quickly done piece of work to make some money.