Turbofan without afterburner
In non-afterburning engines the exit temperature inside the nozzle is around 600°Cexit temperature inside the nozzle is around 600°C at full continuous thrust. If the ambient temperature is low, less heating is needed for the same thrust, and exit temperatures are lower. The maximum temperature for a given engine is, however, independent of altitude and given by the materials inside the engine. In flight the continuous maximum can be higher than on the ground, when the cooling by the external flow is less effective.
Temperature profile at a distance
This report gives results of ground measurements on the Pratt & Whitney JT8D of the Douglas DC-9 and shows how quickly the temperature drops behind the aircraft due to mixing and radiation.
Jet temperature behind a DC-9 at take-off power. Picture source.
Jet temperature behind a DC-9 at idle power. Picture source.
With afterburner
With full afterburner the engine uses approximately five times as much fuel as when running dry, and it shows in the exhaust gas temperature. This report details measurements of nozzle pressures and temperatures on one of the General Electric F-404 engines used in the X-29 program. The plot below is taken from the report and shows exhaust-jet temperature summaries in the horizontal centerline for various power settings (PLA = power level angle; 120° is full afterburner and 87° is military thrust).
Nozzle temperature survey of the GE F-404 afterburning engine. Source.
The test conditions were 30.000 ft altitude and Mach 0.3, simulated in an altitude chamber. The temperatures were measured with a rake just a few inches aft of the engine nozzle. Note that the temperatures are given in Rankine; the maximum of 3800°R is 1838°C. The wake of the engine's center body causes lower temperatures in the center of the jet at XSRL = 0. The nozzle edge is at 12.7 inches from the center; due to symmetry only one half of the jet temperature profile is shown.