I am not just talking about our thoughts about them (deities), but just our thoughts in general, and the things that are in our minds (not talking about religion). I am asking this because deities are omnipresent.
Yes, nothing is hidden from the deities.
O Arjuna! The Lord dwells in the heart of all beings revolving them all by His mysterious power Maya, as if they were objects mounted on a machine.
The Lord hidden in our hearts is called Antaryami and knows all our secrets including our thoughts.
Yes, and this is because God is called paramAtmA, who dwells within every soul. gItA 15.15 says:
sarvasya chAhaM hRRidi sanniviShTo mattaH smRRitir jnAnam apohanaM
I am seated in everyone’s heart, and from Me come remembrance, knowledge and forgetfulness
ChAndogyopaniShad gives specific details about God and the desires of hearts. 1.7.6:
The person in the eye rules the world below him and also rules the desires of the human mind.
He also decides the wishes of the gods and goddesses.
There are a large number of references to God's knowledge of thoughts in the fourth book of the bhAgavata purANa.
vedAhaM te vyavasitaM hRRidi
I know your desire in the heart
sarva-dRRishaM sarva AtmAnaM
He is within everyone’s soul as the witness of everything
vidus taM puruShaM santam antar bhuNkte hRRiShIkair
You know them and know how they are enjoying their senses.
kasmAn no veda nAshiShaH
Why would you not know our desires?
who knows the minds of all