This was posted on a FB forum:
Sigrid Van Dort has a section on crossed beak in the book "Genetics of the Chicken Extremes". There are two types of cross beaks, those that occur at hatch and those that occur weeks after hatch. The latter is the inheritable trait, however it is stated that this is from a recessive gene, but it is not complete. Because on testing, no one was able to produce pure breeding crossed beak birds, even after being heavily inbred. The conclusion was if the rest of the bird is good, do not hesitate to use it to breed because the chance of getting more are small. Now the ones that occur at hatch, that can be caused by a short high incubator temperature. The author did not state how high is high.