Slight revision:
A terminally ill single father romances a vulnerable heiress to?secure a home and future for his son.
"Terminally ill" implies the inciting incident that motivates his action -- what he is incited to do as a result of the diagnosis.
Your logline tells the story from the point of view of the father, which is okay.? But for your consideration, I think there is ?an even more interesting story line?embedded in the concept, that of the son. Who, after all, is the stakeholder, the one who has to live with the consequences of his father's action.? What if the heiress likes him? -- but he doesn't like her?? What if, instead, he prefers his real mother, a woman of modest means who?cannot provide him with the material support and future opportunities that the heiress is all to eager to shower upon him?
What if he likes his ?step-mother and certainly likes? her lifestyle, but the heiress does not like him?but accepts him as part of the "package deal"?? Only to?reject him when the truth comes out about his terminal illness-- as it surely will -- and?she realizes she's ?been conned by his father?
I don't know where you're going with the concept, but I can see many interesting possibilities.? Good luck with your writing.