Flowering is initiated after a cold period. Growth stops at < 8 degrees C. Optimum growth is at 32 degrees C. They can tolerate very low and very high temperatures for short periods but only with adequate irrigation.
"Date palms can grow from 12.7 to 27.5 °C average temperature, withstanding up to 50 °C and sustaining short periods of frost at temperatures as low as –5 °C. The ideal temperature for the growth of the date palm, during the period from pollination to fruit ripening, ranges from 21 to 27 °C average temperature. Dates are widely grown in the arid regions between 15ºN and 35ºN, from Morocco in the west to India in the east (Zaid and de Wet, 2002a)."
This chapter (from Food and Agriculture Organization (FAO), United Nations) has detailed descriptions of the impact of temperatures on the growth of date palm in different regions and countries. The chapter also includes phtos showing symptoms of date palm plants suffering from extreme temperatures.
CHAPTER IV: CLIMATIC REQUIREMENTS OF DATE PALM [ http://www.fao.org/docrep/006/y4360e/y4360e08.htm ]
"Even though date palm is a thermopile species, it withstands large temperature fluctuations. Below 7°C growth stops and this stage is called a resting period. When the temperature decreases for a certain period to below 0°C, it causes metabolic disorders which lead to partial or total damage of leaves. At -6°C pinnae margins turn yellow and dry out (Figures 29a and 29b). Inflorescences are also heavily damaged by frost (Figure 30). When frost periods are suspected, inflorescences should be protected with craft paper bags immediately after pollination (Figure 31). From -9 to -15°C, leaves of medium and outside canopy will be damaged and dry out. If these low temperatures are maintained for a long period (12 hours to 5 days) all leaves will show frost damage and the palm will look as if it was burnt (cases of Morocco date plantations in 1952, and 1965; Iran, 1964; USA, 1913, 1937, 1949 and 1959 (Mason, 1925a; Nixon, 1937). The more leaves damaged, the greater the possibilities of poor fruit quality that year. Poor flowering could also be expected."