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The Master escapes with a fury burning hotter than the fire that was meant to destroy him. The Doctor tried to incinerate him, kill him in such a brutal and definite manner, and couldn't even look him in the eyes as he did it, the coward that he is.
He's burning with indignation and a desire for revenge, but above all, pride. As inconvenient as the Doctor's interference might have been, the Master has returned, which does help temper some of his anger, and more clearly make him consider the Doctor's descent into the sort of behaviour that he likes to consider himself superior to. It won't save the Doctor from his revenge, but there is a certain pleasure in knowing that he's the Doctor's pathway to corruption.
The right thing to do would be to kill him, of course. Not to take a regeneration as he did already, but to properly kill him. He won't, but he can do the same as the Doctor and at least try.
The revenge is in the action, not the outcome, so the Doctor will struggle to regenerate and know that he is the cause, knowing that even away the Master still has power over him.
It's only through his fury that he might be able to do something like this, to use the weaker telepathic senses of this inadequate body, boosted by his own TARDIS, to reach into the Doctor's mind at a crucial moment to stop him from regenerating, but the fool helped him by getting into trouble as soon as he left him to die. And it's only because it's this mind, the only one he knows so intimately, that the Master can reach him across time and space.
He'll have his revenge, with a call for the Doctor’s death.