Waste,
There is no "common" word that means "the ability of a body to lose heat". If there were some common term that were used to refer to the characteristic that determines the rate of heat loss, one might have fed that word to you, but as such, this word would not represent any particular property of the material. Others here have given you properties that are important in determining the ability to lose heat. Let me summarize (while I elaborate upon) their posts.
You want a material property which is responsible for heat loss. Different properties of the material are important under different circumstances.
At high temperatures (T>>T(ambient)), the dominant mechanism of heat loss is through radiation [Astronuc]. The rate of heat loss is proportional to \epsilon T^4, where \epsilon is known as the emissivity [Krab] and T is the temperature [Gonzolo]. Blackbodies are considered perfect radators : \epsilon = 1. The emissivity is reasonably correlated to the absorptance (A) of a material, which in turn is equal to 1-R, where R is the reflectance. So, in general, you can expect a good reflector (most things that are white or lustrous or just reflective) to be a poor emitter, and hence will lose heat slowly. A poor reflector (most things dark or black) will be a good absorber, and thus can be expected to lose heat rapidly[Krab]. This is as close as it's going to get, to your goal of finding a familiar explanation.
When the temperature is no so high, and especially if there air flow (or flow of any fluid, for that matter), then the rate of heat loss if proportional to hA\Delta T, where h is the convective heat-transfer coefficient [Dexter], A is the effective surface area, and \Delta T is the temperature difference [Gonzolo]. This mechanism of cooling is known as (forced) convection [Astronuc]. The quantity h, is however, not so much a characteristic of the cooling object, as it is a characteristic of the surrounding medium (and is related to its thermal contact, flow rate, viscosity and other properties). So, the most important property of a body cooling convectively, is the effective surface area (hence the fins on radiators). Now, if you are interested in the rate of cooling, rather than the rate of heat loss, there is one more property involved. While these two terms appear synonymous, the latter refers to the amount of energy lost in time, while the former refers to the temperature change. The rate of decrease of temperature is inversely proportional to the specific heat capacity of the object. Water cools down slowly because of its large specific heat.
If your object is in contact with another solid or liquid, then the rate of heat loss of the hot body (conduction [Astronuc] becomes important) through conduction, depends on the thermal conductivities of both bodies, the heat capacity of the surrounding body, their geometries, the temperature difference, and the area and nature of contact. As far as geometry is concerned, it's hard to transfer heat through long and narrow sections. A good electrical conductor is usually a good thermal conductor (though the converse need not be true).
So, depending on the surroundings and the temperature of your object, you must determine which is the important property. But in most cases, a small, black sphere will lose heat pretty slowly while a shiny piece of wire mesh will lose heat much faster.
In short, no single word really, but if I had to pick one, I'd go with 'emissive'.