Tues Nedarum 79

A husband can't be Maifer in his heart without explicitly saying so. However, he can be Maykim in his heart and doesn't need to say it.

The Ran explains the reason he doesn't need to explain by Hakam, since we see that Hakam takes effect despite not saying anything. We see this when he doesn't say anything until the next day. since a day passes without saying anything, we see in his heart he wants the Neder to stand. So we have a precedence for doing hakam by not saying anything.

R' Akiva eiger asks: there is no comparison between the two cases. By keeping quiet for a day, he reveals to all that his intent is to make the Neder stand. However, within that same day, just thinking of the Hakam doesn't reveal anything to anybody. So we should revert to the rule that things though in his heart is nothing and doesn't take effect.