It boils down to a GM choice
The Divine Intervention feature is almost entirely GM dependent. If you get the 15% roll after using the feature, the following effect is presented:
The DM chooses the nature of the intervention; the effect of any cleric spell or cleric domain spell would be appropriate.
No cleric spell, or cleric domain spell would have the effect you desire, so it would be the GM's fiat entirely if, how, and to what extent Tempus would choose to/be able to intervene.
Sentient Magic Items
The rules on sentient magic items are fairly vague on how these items are created, or if restoring them is possible. The Dungeon Master's Guide says:
Some magic items possess sentience and personality. Such an item might be possessed, haunted by the spirit of a previous owner, or self-aware thanks to the magic used to create it.
As far as I can tell, it is not clear which of these, if any, has resulted in Hazirawn's sentient from the adventure module, so even if we could reproduce the conditions of its sentience, we wouldn't know which conditions to reproduce. Again, this would boil down to a GM decision on if/how it were possible to reconstitute a sentient weapon, deity or not.
A look at Tempus from a lore perspective
Tempus is a neutral deity, and a god of war. He is well known as a proponent of honorable battles, and especially, honorable/courageous deaths in battle. If Hazirawn sacrificed himself in such a way, Tempus would almost surely respect that sacrifice (a battle against Tiamat is surely a courageous endeavor).
Because of these facts, I don't think the Divine Intervention question is about whether Tempus would honor the request, but whether he is able to. Dan B's answer goes into this a bit, and there are certainly many reasons why a deity would be unable to access the soul/spirit/consciousness of Hazirawn to restore the sword to your barbarian party member.
That being said, I'm sure it is within Tempus' power, as a greater deity, to restore the magical properties of the greatsword. He also, almost surely, could place some sort of sentience in the sword, even if the original sentience is beyond his reach. Perhaps the new sentience of the blade is that of one of Tempus' deceased followers whose soul resides in his realm and is willing to return to the living in some fashion to partake in further battles.
Of course, Tempus' behavior is once again up to the GM, so she is the only one who can answer your question for your group's campaign.