Car will crank over

Hello,

Yesterday my car would not start. I would press the starter button, it would click, but it wouldn't start. All the dash, two screens, auto adjusting seats would function. My phone would even charge and I could Bluetooth audio. I got a jump and it started after two to three minutes on. I drove it to the dealership and they said it was the battery. They checked the starter and the alternator and said that they were fine. They replaced the battery and the car started fine and I went home. I woke this morning and it started, I went to work for an hour or so, came out it started up fine, and I drove home. Three hours later (after it had been in the sun) I went out to leave and it did the same thing, just clicked and not starting. I am lost. If the car jumps and starts, and works for a bit then wont start again. What could it be?