Actually, regardless of whether you have bags, you have to go through immigrations and customs.
Since the UK is your first stop outside the US, you have to clear immigrations no matter whether you are connecting to a domestic or international flight or staying in the UK. Where you go through, depends on what connection you need to make - i.e. which terminals.
You would only avoid customs if you had a bag that was checked through. But if you are on non-connecting flights, you have to re-check in at the desk, so you go through customs - probably terminal 3 or 4, before re-checking any bags.
3.5 hours should be plenty of time unless the international flight has a reputation for being late - I had a late flight and then we had a wait for a gate. If you do think you are tight on time, don't hesitate to make this known if you end up in a line at security etc., because they are usually good about letting you get through ahead of the line if you need to make a flight.