What's the difference between EMSE vs. IMSE when buying components? (Linear Technology parts?)
See the datasheet (page 4, note 2):


  The LTC3388E-1/LTC3388E-3 are guaranteed to meet
  specifications from 0°C to 85°C junction temperature. Specifications over
  the –40°C to 125°C operating junction temperature range are assured by
  design, characterization and correlation with statistical process controls.
  The LTC3388I-1/LTC3388I-3 are guaranteed over the –40°C to 125°C
  operating junction temperature range.


In short, both can be used over the full -40°C to 125°C range, but only the parts with an I have the specifications guaranteed over the full range (possibly meaning binning).