Welcome to the Punto club! Acts the same way as headphones do, plug it in and play tunes like you say!
Have you tried switching to AUX mode on the stereo? If it's the OEM Blaupunkt radio, it's activated by pressing CD twice bizarrely. Check for Blue & Me like Macaulay said too, that can be a pain in the proverbial from what I hear.
Also, it's easy to miss that with Auxiliary both the iPhone audio and stereo volume are in play. I'd advise whacking your stereo volume to 5 and phone volume to the max when plugged in.