making a sourdough starter in desert like conditions
Well every yeast strain is a bit different but normally the range is fairly forgiving.  Speaking from homebrew side; killing yeast from cold is almost impossible. 

Homebrew side; they make electric thermostat controlled blankets to control temperatures; if you are going repeat this a couple times might be worth investment.  In beer world; changing the yeast reproduction rates and brew temp can have significant effect on flavour; not sure this applies to sourdough starters at all.   

Temperatures:

above 108F - yeast start to die

140F - all yeast dies

below 32F - yeast can die

40F-65F - most yeast strands will be sleeping / dormant

78F - usually optimized production

Now I see optimized production of CO2 change from 10-15 degrees depending yeast strain; some being as high as 100; others being low as 70; but gives a good idea.