Bobby took care of noting that density is a function of temperature AND pressure, so I'll take a bit of a different view. A vertical profile of virtual potential temperature would help explain it a bit too. Let's assume an unsaturated air parcel... If the environmental lapse rate is less than 10C/km in magnitude (i.e. 5C/km), a parcel that's forced to rise will be colder (more dense, technically) than the surrounding environment. This negative buoyancy will cause the parcel to accelerate downward. For what it's worth, the now descending parcel will tend to "overshoot" its original level, being pushed downward, where it will be warmer (less dense) than the surrounding environment. Now, it will accelerate upward again, and so on, in an oscillating manner. Such a process demonstrates thermal stability -- no matter whether the parcel is originally forced upward or downward, it will be forced back to its original level. If virtual potential temperature increases with height, there is implied stability for an unsaturated parcel; virtual potential temperature that is constant with height is nearly equivalent to dry adiabatic lapse rate (~9.8C/km), so virt. pot. temp. that increases with height signifies that the temperature decreases with height less than the dry adiabatic lapse rate. Vertical changes in mixing ratio affect the density of the parcel too, which is important to keep in mind too, and it is the reason why we look at the virtual temperature when trying to assess 'dry' stability.
But what happens if the environmental lapse rate is greater than 10C/km in magnitude? Suppose, for example, that the temperature at 1km AGL is 20C, and the temperature at 2km AGL is 0C, representing an environmental lapse rate of 20C/km. If the parcel at 1km is pushed upward to 2km, its temperature will be 10C. Uh oh -- the parcel temperature is 10C higher than the ambient temperature, and this positive bouyancy will result in an upward acceleration. These "superadiabatic" lapse rates are relatively common immediately above the surface during the day (assuming there's sunshine). The lapse rate between 1mm above an asphalt parking lot and 10 m above that parking lot can be much, much greater than the dry adiabatic lapse rate. In such cases, auto-convection occurs -- the "air" immediately above the asphalt accelerates upward, while the air farther above the asphalt sinks (in a way, to fill the "void" caused by the rising near-surface air)... Imagine a pot of water on the stove -- water at the bottom of the pan, immediately adjacent to the heating element, is heated more quickly and to a higher temperature than the water at the top of the pot. If you watch closely, you'll see convection in action.
FWIW, similar things happen in the boundary layer when the sun rises and diabatic heating commences. Sensible heating at the earth's surface leads to the creation of what we call the "convective boundary layer" (CBL). As solar heating continues, the boundary layer tends to deepen (air mixes from above as heated air at the surface rises, leading to the familiar characteristic of boundary layers -- constant potential temperature and mixing ratio with height, at least above the surface layer). I'm going off a tangent here, so I'll stop.
