Is there any research about possible biological preconditions of mentioned theories?
The four temperament theory is an ancient theory of personality; however, it does appear to have been the dominant theory of personality from 400BCE through to the mid 1800s. New theories of personality emerged with Darwin's observations on emotion and Galton's proposal of the lexical hypothesis. The lexical hypothesis is foundation of many of the current theories of personality, the most popular of which is the five factor model.
More recent temperament theories such as MBTI, DISC have been criticised for a lack of scientific basis and being Barnum tests. Barnum tests are such that everyone is happy with the result, i.e. Are you either intelligent or clever? MBTI and DISC seem to omit the less attractive aspects of humanity, such as: narcissism, anger, anxiety, depression etc. On this basis, research of temperament is infrequent.
A criticism of psychological theories in general (not just temperament theories) is that the neurobiological basis remains unidentified, see here and here. An active area of current science is to establish the neurobiological basis of personality and progress is regularly reported.