Have no idea here. I translated it on google but yeah it's not that trustworthy I know. Somehow I found out the word "passio","ad" and "sanationem". We are going to use it as our school of medicine motto, so if you have any suggestion or idea please let me know.
I suggest cupiditas sanandi or cupiditas medendi.
The noun cupiditas means a 'passionate desire, longing, yearning.' For example, in the Pro Sulla (40), Cicero says, o di immortales...vos profecto animum meum tum conservandae patriae cupiditate incendistis, 'Immortal gods...you inflamed my heart with a passion for preserving the state/Republic.'
For a slightly softened expression, one could use studium, 'eagerness,' 'enthusiasm' instead of cupiditas.
Sanandi/medendi is the genitive of the gerund. This is a so-called objective genitive, which is often found with nouns that describe emotions or actions to indicate the thing or person that the emotion/action is directed toward.