We examined the combined impacts of future increases of $CO_2$ and temperature on the growth of four marine diatoms (Skeletonema costatum, Chaetoceros debilis, Chaetoceros didymus, Thalassiosira nordenskioeldii). The four strains were incubated under four different conditions: present ($pCO_2$: 400ppm, temperature: $20^{circ}C$), acidification ($pCO_2$: 1000ppm, temperature: $20^{circ}C$), global warming ($pCO_2$: 400ppm, temperature: $25^{circ}C$), and greenhouse ($pCO_2$: 1000ppm, temperature: $25^{circ}C$) conditions. Under the condition of higher temperatures, growth of S. costatum was suppressed, while C. debilis showed enhanced growth. Both C. didymus and T. nodenskioldii showed similar growth rates under current and elevated temperature. None of the four species appeared affected in their cell growth by elevated $CO_2$ concentrations. Chetoceros spp. showed increase of pH per unit fluorescence under elevated $CO_2$ concentrations, but no difference in pH from that under current conditions was observed for either S. costatum or T. nodenskioeldii, implying that Chetoceros spp. can take up more $CO_2$ per cell than the other two diatoms. Our results of cell growth and pH change per unit fluorescence suggest that both C. debilis and C. didymus are better adapted to future oceanic conditions of rising water temperature and $CO_2$ than are S. costatum and T. nodenskioeldii.