In this paper the annealing of Na colloids in heavily irradiated NaCl with damage levels up to 10 mol% is discussed. Recently the melting properties of Na colloids in heavily irradiated NaCl have been studied using differential scanning calorimetry. The observation of three endothermal latent heat peaks, numbered 1, 2 and 3, as a function of the dose, has been reported. Here we discuss the annealing behaviour of heavily irradiated crystals doped with KBF4, which show a large melting peak 3. The changes in the appearance of the latent heat peak provide us with information about the properties of the sodium colloids. The annealing of the colloids in two different temperature ranges is described. At moderate annealing temperatures between 160 and 210 degrees C the peak shifts with annealing time to lower melting temperatures very rapidly. The shift of the peak is activated by an energy of 1-1.4 eV and strongly depends on the initial amount of latent heat. At high temperatures between 250 and 320 degrees C a decrease of the latent heat is measured, due to the back reaction between Na colloids and molecular Cl2. After continued annealing at high temperatures the melting behaviour becomes very anomalous. The melting peak splits into two peaks, the main peak and a new, sharp one arising at 92 degrees C. After the splitting of the peak the back reaction slows down significantly, activated by an energy of 1.2+or-0.3 eV. Both the moderate- and high-temperature annealing behaviour indicate that the processes are very local, with a short length scale of the order of 1 nm. This implies that the morphology of this type of colloid is highly irregular, with a dense and fine nanostructure.