CelsiusCelsus (c. 25 BC – c. 50 AD) often uses the intransitive verb sanescere in his De Medicina to getexpress the non-causative change of state meaning.
Insanientes sub somno sanescunt (Cels. 3, 18).
Unlike sanari, which is in principle ambiguous between a passive interpretation (involving an (implicit) agent/cause: "by someone/something") and a middle one (cf. Draconis's answer), notice that sanescere is not ambiguous. So sanesces/sanescetis is a better translation for 'You will heal' if an internal process is involved.
As for the use of adjuncts pointed out by Draconis, here are my choices/preferences: tempore is compatible with both sanari and sanescere, whereas therapia is probably better with sanari (NB: only the latter involves an external cause).