Suppose some part of the planet in question (possibly an inaccessible region like a high plateau or the poles; whatever your plot dictates) is covered by what amounts to an enormous oil-field. Perhaps millions of years ago, a large and fertile algal sea dried up and was buried by some geological event.
Now, in the (geologically) recent past, something has suddenly uncovered a significant fraction of the oilfields. Could be tectonic activity, an asteroid impact, or anything else that suits your plot. After the really volatile stuff in the crude oil (methane, ethane, propane, butane, hydrogen sulfide, etc.) has evaporated (and perhaps been consumed by microbes or flora), there'd be a period when the slightly-less volatile hydrocarbons would evaporate. Hexane, for instance, fits your temperature requirements pretty well, it doesn't mix with water to any significant degree, and its solvent properties would make it very easy to distinguish from water rain. It's slightly toxic, and it's a nervous-system depressant, which would have to be worked around.
Another possibility, springing from the same root idea of suddenly-exposed petroleum reserves, is a massive oilfield fire in some inaccessible part of the planet in question. This could give you a couple of different types of rain/precipitation. The volatile stuff (anything natural-gas-, gasoline-, or diesel-fuel-equivalent) would boil off and burn pretty early on, but if the fire decreased to a lower intensity after that, it could evaporate analogues to heavy fuel oil, which could be carried by a jet stream or similar until the droplets coalesce sufficiently to rain out. Or, the precipitation in question could simply be "snowflakes" of fine soot which aggregated in the upper atmosphere. In both cases, it'd be very distinctive black precipitation. Tarry oil in the fuel-oil case, and black graphite snow in the soot case.