All other things being equal, I would say that potassium nitrate (KNO3) has a higher degree of thermal stability. It melts at 333 degrees Celsius, whereas lithium nitrate (LiNO3) melts at 279 degrees Celsius. Lithium, atomic number 3, is also a smaller atomic nucleus than that of potassium, atomic number 12. Atoms that have larger mass in their atomic nuclei are generally more stable than those that are smaller. Lithium is also in group 1, which are classified as alkali metals, which tend to be more unstable as a group as opposed to potassium, which is in group 2, the alkaline earth metals. Group 1 elements have one electron in their outer shell, while elements in group 2 have two, which tends to make them a little more stable.
Since the lithium ion has a higher polarizing power and is smaller than potassium and the potassium has a lower charge to volume ratio than the lithium, I would say that the potassium nitrate is more thermally stable. The cloud of the nitrate ion seems like it would be more easily distorted by the higher polarizing power of the lithium than it would be by the lower charge density of the potassium. Hope this is a help.