Nonlethal damage doesn't actually interact with temporary HP at all
Dealing Nonlethal Damage: Certain attacks deal nonlethal damage. Other effects, such as heat or being exhausted, also deal nonlethal damage. When you take nonlethal damage, keep a running total of how much you've accumulated. Do not deduct the nonlethal damage number from your current hit points. It is not “real” damage. Instead, when your nonlethal damage equals your current hit points, you're staggered (see below), and when it exceeds your current hit points, you fall unconscious.
So if you're a 6th level telekineticist with 2 burn invested in Force Ward, you would have 12 points of nonlethal damage and 12 temporary HP. If you had 72 HP, say, the first 12 damage that you take are deducted from your temporary pool, and if you take 61 more damage you would be unconscious at 11 HP.
Just wanting to figure out how burn damage works for a Kineticist when they have temporary HP from spells such as False Life or Death Knell. From my understanding by RAW you would loose these temporary HP first.
If you mean a Telekineticist with Force Ward, temp hit points from Force Ward are used first before any other source of temp hit points. Says so in the description of Force Ward.
You constantly surround yourself with a ward of force. You gain a number of temporary hit points equal to your kineticist level. You always lose these temporary hit points first, even before other temporary hit points. If an attack deals less damage than you still have as temporary hit points from force ward, it still reduces those temporary hit points but otherwise counts as a miss for the purpose of abilities that trigger on a hit or a miss.
And what happens if you have temp hit points and then take burn? You take the non-lethal damage and do not use the temp hit points.
For each point of burn she accepts, a kineticist takes 1 point of nonlethal damage per character level. This damage can’t be healed by any means other than getting a full night’s rest, which removes all burn and associated nonlethal damage