That he may dip (hina bapsēi). First aorist active subjunctive of baptō, common verb, to dip.
In water (hudatos). Genitive, the specifying case, water and not something else.
Cool (katapsuxēi). First aorist active subjunctive of katapsuchō, a late Greek compound, to cool off, to make cool. Only here in the N.T. but common in medical books. Note perfective use of kata- (down). A small service that will be welcome.
For I am in anguish (hoti odunōmai). The active has a causative sense to cause intense pain, the middle to torment oneself (Luk 2:48; Act 20:38), the passive to be translated as here. Common verb, but no other examples in the N.T.