For the little ones (up to about 8Ah, I think) I've worked with, yes, they do--and as soon as the reach the point at which they begin heating, their voltage drops, which is what causes the heat (energy has to go somewhere).
So once the voltage drops, then the current flow into them increases, heating them even further, which can cause a runaway condition, and fire (or even explode the cells if they begin venting faster than the cell's vents can handle).
This is why it is generally a bad idea to parallel NiCd or NiMH, because whichever cells get full first will then start sucking power from the other paralleled cells, and heat much more than they would otherwise, with probably bad results, depending on number of parallel cells, capacity, charge state of those cells, pack construction, etc.
It is also why typical consumer-level NiCd / NiMH chargers have at least one (sometimes both) of two methods of charge shutoff: delta-V, detecting the drop in voltage, and delta-T, detecting the spike in temperature. Either one will trigger charger cutoff.
That's all for consumer-level stuff, RC stuff, etc., ebike packs, and so on; what I have my experience with.
I had a pack that while it didn't catch fire, it overheated severely when the thermistor the Tenergy charger depended on to determine end-of-charge (it didnt' do delta-V, apparently), had an intermittent connection that in this case worked during charge start when it tests that thermistor, but failed somewere during charge itself, so that when the cells heated, the charger never stopped trying to charge them. If I had had them enclosed in a box with no airflow, it's quite possible there *would* have been a fire. As it was, the pack was severely damaged.
I have no idea how the BMS in the car deals with all this, or if indeed it even ever charges the cells up that high in the first place; it may deliberately never give them a charge long enough to let them reach that topped-off state, just so the car doesn't have to deal with the heating problem, and potential fires from failure of the system to cutoff charge when it gets hot.
There are a few threads around here (and DIY Electric Car) about the packs in those cars and how they work, if you look around.