How can I boil an ostrich egg to ensure it is soft boiled?

You can't easily get a set white and a runny yolk, but 62.5°–63° (145℉) for 3.5 hours gets a cooked yolk that's still runny; the white will not be set, however.

You may be able to get a soft-boiled ostrich egg with two-phase cooking though.

The fundamental problem is that ostrich yolks coagulate at a lower temperature than ostrich whites. Thus if you just cook to a constant temperature inside, by the time the whites are set, the yolk will also be set.

Ostrich egg whites do not coagulate the same as hen egg whites, but the yolks seem relatively similar; thus you can follow hen egg guidelines for the yolk, but the white will be off.

I tried cook sous vide at 64° (~147℉) for 6 hours, and ended up with an egg with the yolk fully set, but a gelatinous white: almost the opposite of what we were looking for!

For another attempt, you can see Nicole Miizuka: The Ostrich Egg, who cooked it at 145℉ for 3 1/2 hours, and got a runny yolk (and runny white).

I found a paper discussing this: Gelling and color properties of ostrich (Struthio Camelus) egg white, and it found that at 65°, hen egg white rapidly coagulated completely, but ostrich eggs only coagulated to 70%.

Thus, if you'd like to have a soft-boiled ostrich egg, I believe you would need to cook it for a long time (3 or 4 hours?) at ~62.5° for the yolk to cook, and then raise the temperature to close to boiling, but only leave it for a brief time (10 minutes?), so the white sets, but the yolk stays liquid.