The XCOM Wikia Temple Ship Assault page mentions that one could take a Field Medic Support to get medikits that heal 10HP. Below is the quote:
At least one Field Medic Support with Savior and Improved Medikits (for option to heal 10 HP) will likely be crucial for survival and mission success.
After completing the Improved Medikit Foundry project, one gets the health recovered by the use of a Medikit increased from 4 to 6.
How do I get the medikit improvement from 6 to 10HP?