There would seem to be quite a lot of missing records for your Tempests for the period of time we are looking at here.
You say Michael was born in 1715. Have you found that record, or is this an estimate? I couldn't find this.
Also, as you say, no marriage of a Michael to a Judith Cator at any date. The only 2 marriages that come up on any site for a Michael are later in the 1760s and 1770s.
There was a 'Judith Cater' baptised 5.8.1677 at Allestree, just a couple of miles from Duffield, but this is too early to be marrying and having children in the 1730s and 1740s. At some point may be the same family though.
There is a burial of a 'Mary Tempest' 16th June 1733 at Duffield, wife of Michael. His residence is 'Burley'. Difficult to say if this is a wife of your Michael. He would only be about 18 by then with a birth date of 1715. I suspect a Michael from the next generation.
I expect you have seen the wills of your Michael died 1778, and his father died 1738. They are both of Burley, Duffield. Possibly the Mary that died in 1733 was your Michael's mother.
Interestingly, in the will of Michael 1738, he has a daughter Dorothy married to John Wall of Allestree. They married 7.4.1726. She is given as 'of Burley'. John Wall is one of the appraisers of the Inventory for this Michael (which is worth seeing if nothing else for it's highly unconventional spelling!).
There is a will of a john Tempest in 1759, who is your Michael's brother. He is also of Burley.
Interestingly he has daughters Dorothy and Judith. These would seem to be family names, but it's not evidence for a Judith though.
All these wills on findmypast.
Duffield registers are on film on familysearch. You could browse through them page by page if you think it would be worthwhile. You need to register - free and pretty easy, and then luckily these Derbyshire records can be viewed from home - not always the case at all. Often you have to go to n LDS library to view the films. (Go to search -> catalog-> place name : Duffield -> church records -> parish registers)
Good luck!