It all depends on the agency and their response plans.
In general, "hot" means lights & sirens, and "cold" means no lights, no sirens, following normal traffic rules & flow.
In a structured dispatch system, cold responses generally indicate the absence of life hazard or high property hazard at an incident. For example, my agency goes cold to non-injury MVCs with fluid pickup only, carbon monoxide alarms without illness (as ibagli said), confirmed false alarms at automatic fire alarm incidents, etc. Hot responses are reserved for things like cardiac arrest, traumatic injuries of more than trivial (toe, finger, wrist) nature, confirmed or possible fires, dangerous goods spills/leaks, etc. Even on automatic fire alarms not yet confirmed false, only one truck goes 'hot' while the others go 'cold'. The reason for this is that so many alarms are false that we don't want to risk an accident while responding 'hot', so we minimize the 'hot' response - but still attend in a timely fashion, in case the alarms prove to be real. Of course, if the first truck gets there and says "Holy #(%@ it's rippin'!", we can certainly upgrade the response of the other trucks.
