The tooth itself, even though it is cracked, is part of your body and thus is not a
chatzitzah.
A properly made temporary crown (also called a cap) is generally meant to be in place for a week or more, and as long as it is well-placed and comfortable, is also not a chatzitzah.
In your case, a temporary crown will probably be removed and put back after each step, until placement of a permanent crown. It would be preferable for mikveh immersion to take place at least 7 days before the appointment for placement of the permanent crown. However, as long as the temporary crown in still comfortable and sturdy, it is permissible to immerse at any point in the process.
It may not be wise to delay the procedure indefinitely, as an inadvertent bite on a hard object can lead to a much more extensive problem.
This response was updated 21 December, 2025.