Humans sense temperature differences.
(Including edits based upon comments)
Because the question is "Do humans perceive temperature or heat-flux?", I will answer the answer from a psychophysical perspective, i.e., by dealing with sensory awareness.
Just as with many other sensory systems, temperature sensors in the human body adapt to ambient stimuli (i.e., constant absolute stimulus levels). In other words, after being exposed for a while to a certain temperature, one looses the perception of temperature per se (assuming temperatures are within comfortable limits of course, otherwise general discomfort will arise such as shivering or sweating etc.).
Therefore, temperature sensing in humans is not absolute, but differential, and occurs when differences occur relative to the baseline.
Holmes and Wood (1968) mention in their Introduction the following, and I quote:
...three variables of thermal stimulation [...] affect the sensitivity of human subjects to warm and cool stimuli. These are (1) the temperature to which the skin has been adapted, (2) the area of skin over which the thermal energy is applied, and (3) the rate at which the temperature of the skin is changed.
Variables (1) and (3) clearly emphasize the differential nature of temperature perception in humans. Variable (2) is a general psychophysical phenomenon, and basically shows that when a stimulus is sufficiently large, temperature differences will be more easily felt, while when the skin surface being stimulated is excessively small (say a needle with a small temperature difference is pressed against the skin) certain temperature differences may not be felt any longer.
With regard to your question on metal and whether heat-flux can be sensed: a metal surface will feel cool only when it is lower in temperature than your body. Suppose now you touch a metal object at room temperature, i.e. lower than your body temperature. In that case, as you already indicate, it will draw away heat quickly from your skin by conduction, creating a 'heat-flux' if you like. The extraction of heat thereby elicits a powerful stimulus, because a large temperature difference creeps into your skin as heat is drawn away from your skin and underlying tissues. As such, and contrary to other answers given elsewhere, I explicitly say yes, 'heat-flux' can be sensed as it per definition generates a temperature difference. This in contrast to touching insulators like wood or plastic, which will quickly adopt the temperature of the skin very locally where you touch it. However, as has been pointed out by others - this does not mean that temperature is measured by heat-flux sensors per se. In contrast, temperature is measured by temperature sensors that detect temperature differences (differential stimuli) between skin and external media. Because a temperature change is also a differential stimulus, it will also be detected, and hence 'heat-flux' will therefore be detected as well.
Holmes & Wood, Perception & Psychophysics 1968; 3:81-4