A few things:
- shutting itself down
- not turning back on
- pixel errors (pixels not going to the colour they should be)
If you have any of these issues, call up dell's technical support line, ask for the monitor department, tell them your issue and they should have a replacement monitor at your door the next working day (dell monitor warranty and general CS for monitors is great). That said, please don't worry - the monitors being warm does not mean any of the above things will happen - it is most likely a by-product of the backlight brightness being set very high out of the box (AFAIK these monitors have a peak power usage of ~111W).
Also, make sure you either keep all your original monitor boxes or make a note of the "Dell Works Order Number" which is written on a sticker on the side of your box. This number is absolutely required to make use of your warranty - get hold of it and keep it safe.