Photobiological hydrogen production by nitrogen-fixing unicellular cyanobacteria has long been considered to be an environmentally sound and very promising method for the future supply of renewable clean energy. Using six Korean nitrogen-fixing unicellular cyanobacterial strains and the Synechococcus sp. strain Miami BG043511 we performed cultivation experiments to find out the strain-specific optimal temperature for population growth and $H_2$ production. Under $20^{circ}C$ the population growth of all the tested strains was significantly retarded in contrasts to the faster and higher growth under 25, 30 or $35^{circ}C$. The highest growth rates in all the 7 strains were measured under $30^{circ}C$ while the maximal biomass yields were under $30^{circ}C$ (strains CB-MAL 026, 054, and 055) or $35^{circ}C$ (strains 002, 031, 058, and Miami BG043511). The difference between the maximal biomass yields at $30^{circ}C$ and $35^{circ}C$ was not greater than 10%. The quantity of photobiologically produced $H_2$ was only slight larger under $35^{circ}C$ than that under $20^{circ}C$. Our result may suggest a two-step process of $H_2$ production which includes rapid and sizable production of biomass at $30^{circ}C$ and the following high $H_2$ production at $20^{circ}C$ by the test strains of marine nitrogen-fixing unicellular cyanobacteria.