The Bible is quite clear that only God can read the heart (1 Kings 8:39). What that has to do with praying in silence, I have no idea. Is he frightened of Satan hearing him pray ... or of his neighbour?
There is no better armour against the devil than prayer. He hates that. He can't stand it.
When man speaks to God in the Scriptures, he doesn't whisper, or project his thoughts, he speaks ...The Book of Job is an extended contemplation of the question of theodicy. It's clear the Adversary suspects he can make Job curse God, but he does not know ... and as it turns out, he's wrong.
Because God does know the heart, whether one prays in silence or aloud is immaterial. In fact, when it comes to knowledge of the heart, the Christian Tradition is quite clear that God reads in the heart that which goes beyond words.
It matters not to God, but it matters to us, and for the reasons posted above, praying aloud is then, for certain contingent and secondary reasons, in some ways the better way. There is a long esoteric tradition on this, and it also leads into areas such as the invocation of the Divine Name (or indeed, the invocation of evil spirits). The point being the term 'invoke' comes from the verb 'vocare' to call – and again there's a long tradition of the power of the spoken word over the thought word. Thought words have no substance, spoken words have being.
Prayer, like anything else, is something one gets better at the more one practices. And an accompanying physical practice embodies better and quicker than just mental practice.
When Christ says: "But thou when thou shalt pray, enter into thy chamber, and having shut the door, pray to thy Father in secret" (Matthew 6:6), it does not necessarily mean pray in silence – indeed one can pray in silence anywhere – esoteric instruction aside, the advice to 'enter into thy chamber' is to remove oneself from earshot. When Christ prays in Scripture, He prays aloud. I can't think of anywhere in Scripture where the person prays 'in his/her head'.
Satan is not omniscient. According to an ancient Christian tradition, there are three 'mysteries ... accomplished in the silence of God' of which Old Nick was unaware. But again, according to Scripture, Satan and his minions were in no doubt as to Christ's true identity – it's they who address Him as 'the Son of God' and not in any metaphorical sense.
Whilst Satan cannot read the mind, he can read human nature – he's had enough practice – and he knows weakness, because he himself is weak. and he sees with a spiritual sense, so more astute than our fallible physical senses.
The flaws we see in others, we see because they are our flaws ... one of the most powerful life lessons I've ever learned.
He knows how to play humans. The Traditions are full of stories, it's by the the little things that he gains entry, and once he's in, he's in. They're there in Christian teachings, and the Buddhist story of the monk trapped by demons and faced with three sins, each one worse than the one before. The monk chooses the least sin, but then goes on to commit all three. The moral of the story is there is no such thing as a little sin, and Old Nick uses the little ones to open the way to the big ones.
The Greeks call this
logismoi in their spiritual psychology.
So no ... he cannot read our thoughts, but he can read human nature like an open book.
There's a story about Old Nick sending three young demons to tempt a hermit called Antony. For days they try. The rot his food and foul his water so he hungers and thirsts. They parade visions and temptations passed the old man, but he stands resolutely against them. They try every weapon, to no avail ... Eventually they go back and admit there's nothing they can do, Antony is too strong.
'Idiots', says Old Nick. 'Watch'.
He turns up at the old hermit's hut in the guise of a traveller, and stays there three days. He is respectful, helpful, a delightful guest. Eventually it is time for him to be on his way. He's just shouldering his bag when he turns. "Oh, I knew there was something!" he says to Antony with a smile. "I have news of your little brother. He's been made bishop of Alexandria!" And with a wink to his minions, he walks away.