History of the star: Theemim is upsilon¹ in the River Eridanus. Very close to upsilon¹ is upsilon².

[Staal calls upsilon¹ "Theemim", and upsilon²; "Beemim". Allen calls upsilon¹ and upsilon² together "Themim"; and upsilon³ and upsilon⁴; "Beemim"]. There are actually seven upsilons in Eridanus; upsilon¹ - upsilon⁷. Allen says: Theemim is perhaps the Arabic Al Tau'aman and the Jewish Teomim, "the Twins", from the pairs upsilon¹, upsilon², and upsilon³, upsilon⁴. There was uncertainty whether Theemim was derived from the foregoing or from an Arabic term for two medicinal roots; others suggested that it is from the Hebrew Bamma'yim, "In the Water", which would seem more reasonable, although we have but few star-names from Judaea, and it was thought that it might be a distorted form of Al Thalim, "the Ostrich". The Almagest of 1515 has Beemun; and the Standard Dictionary, Thee'nim. 

[Star Names, Their Lore and Meaning, Richard Hinchley Allen, 1889]. 

The astrological influences of the constellation: According to Ptolemy all the stars with the exception of Achernar are like Saturn. Eridanus gives a love of knowledge and science, much travel and many changes, a position of authority, but danger of accidents, especially at sea and of drowning. (Fixed Stars and Constellations in Astrology, Vivian E. Robson, 1923).