The addition of swirl to a non-premixed flame is known to increase the fuel-air mixing rate, which can cause local premixing and thereby increase flame temperature. The present paper quantifies how the flame temperature increases as swirl is systematically increased; it also quantifies how the flame temperature decreases as fuel jet momentum is increased. Of particular interest are two limits which have not been studied previously in much detail. At the high swirl limit, the temperature levels and profile shapes in the non-premixed flame become similar to those of the premixed swirl flame studied by Gouldin. Thus the rapid internal mixing makes the non-premixed flame behave like a premixed flame. A second limit of interest is the transition from a cooler "jet-like" flame to a hotter "strongly recirculating" flame; the temperature change during this transition is reported and the critical level of swirl and fuel jet momentum required to cause such a transition is quantified. Temperatures were measured using non-intrusive laser Rayleigh scattering. It is shown how temperatures can be controlled by systematically varying the swirl and fuel jet momentum, while maintaining good flame stability, which is an advantage of swirl flames over simple jet flames. The paper also quantifies the level of unmixedness, as characterized by temperature fluctuations, in the limit of very high swirl. Even at high swirl the non-premixed flame does not become "well stirred;" temperature fluctuations remain significantly larger than those of the premixed flame reported by Gouldin. A numerical model that includes swirl and combustion is used to help understand the complex balance between centrifugal, inertial and pressure forces.