The temporary crown gives a rough guide as to the likely thickness of the final permanent crown.
When the permanent crown is tried in for fit, then any adjustments are made before cementing. The thickness of the permanent crown must be correct before cementing - if too thin, then more tooth needs to be removed, a new impression taken, a new temp crown made, and a new permanent crown made. This is not costed to the patient as it would indicate the dentist miscalculated way back at the first preparation.
A leaking temp crown lets fluids get inside and will often cause sensitivity.