Imagine you are making lemonade (oxalic acid solution) and adding purple grape juice (KMnO4) drop by drop.
Each drop of grape juice (KMnO4, purple) you add instantly turns colorless because the "lemons" (oxalic acid) react with and "bleach" the grape color — the purple MnO4- is reduced to nearly colorless Mn2+.
You keep adding drops, and each one disappears immediately. The "lemons" are doing their job.
Then, one drop — the endpoint drop — does NOT disappear. It stays faint pink. This happens because all the "lemons" (oxalic acid) are gone. There is nothing left to decolorize the KMnO4.
That faint pink persistence is the endpoint. You don't need a separate dye (indicator) because the KMnO4 IS its own indicator — it's purple when present, colorless when reacted.
Why 60–70 °C? Imagine the lemons are frozen (cold oxalic acid). The reaction happens too slowly — you add a drop of grape juice and it takes 2 minutes to disappear. This leads to a false early endpoint. Warming (60–70 °C) speeds up the reaction so each drop decolorizes in a few seconds, allowing accurate endpoint determination.
Why not above 70 °C? Hot lemon juice can evaporate (oxalic acid decomposes: H2C2O4 → H2O + CO2↑ at high temps). If your "lemon" quantity decreases due to decomposition, you'll need less grape juice to reach the endpoint — a falsely low result.