What is a "biological-only" father called?

Solution 1:

I'm not sure why no one has said it, but the best answer is right in your question:

I may have inherited a heart condition from my biological father.

I have a situation similar to the one you describe, and my whole life this phrase has never failed to convey the meaning of the genetic-only relationship.

Solution 2:

If you're looking to emphasize his lack of involvement, a common description for a father-by-biology-only is: "sperm-donor". (US)

Note that this term is often used outside the context of a formal sperm donation arrangement, usually pejoratively, emphasising that biological father did not provide a parenting role.

Solution 3:

Try birth father also called a biological parent. It means a biological mother (birth mother) or biological father(birth father).

Here is a definition from another site. This site defines it as the man who was someone’s father when they were born rather than the man who has adopted them. It is closer in meaning to what the op asked.

Solution 4:

I've heard "absent father" used in this situation.

In fact, parental absence or absenteeism is recognised in psychology.