Being familiar with the various different kinds of heaters I am curious when you say "diesel heater" because the only two types I am aware of that would fit into this type of description is the first which is the most common, the Kerosene heater which is used in most household types of heating situations, and the Nipco Heaters which are used for heating things like garages and larger areas. Kerosene is suppose to burn cleaner than diesel as far as the fuel grade goes, and I can tell you from years of burning kerosene for heaters inside it is sooty and dirty and there is even an additive bottle that comes in one of four scents just to help it burn less sooty and less of that kerosene smell inside. My negative ion generators can't even be ran when burning it because of the soot they will extract from the air can then be ignited by the static charge of the commercial built for home use negative ion generator that plugs into the household's electrical, so that gives the very clear impression the soot can still pose a fire hazard. It will collect as dust as an oily grime throughout the entire building, including the soles of your shoes as you will notice with time. Plants over time will start to get a shine to them after you try to wipe the oily dust that collects on their leaves, and in time the plants will slow down and have more issues and troubles. I've also tried the air purifying cleaners like for HEPA filtration to cut down on issues, but all it did was plug up 30-day HEPA filters in 2-3 weeks, and the charcoal filters needed to be changed more often as well, overall not happy.
As far as the Nipco Heaters go, they stink more so than the kerosene heaters, but put out a massive amount of heat ahead of itself, great for heating large areas, but they leave things rather drafty when they aren't being used constantly and then if they are they get so super hot in there. The only other idea I come up with under the idea of a "diesel heater" is the house style, but they call that Fuel Oil... and even when I think of the lanterns I keep thinking they have them in Kerosene, White Gas, Lamp Oil... The only diesel heaters I know of that actually run diesel is the Nipco Heaters.
If you are looking for precious control consider looking to a wall mount propane garage heater the type that is "Vent Free" so you can run it off a propane tank, you can get them from running small propane bottles to the 20# propane bottles, up to the LP propane wall mount heaters all in Vent Free. What that means is the CO2 is then released into the air of the location of the heater itself, as such they are now built with CO2 shut offs, if the CO2 levels get too high on a "construction heater" or "garage heater| they are set to automatically cut the fuel supply before it hits dangerous limits for a human or pet. The plants love the additional CO2 and propane burns clean only adding humidity to the air, which offsets for the drying of the air in some cases, other times you still need to add more humidity still.The other style is to vent the heater outside, but since plants need CO2 why not give it to the plants.
Having lived with the different methods of heating for many years, if you are doing anything with plants you will find propane heaters are the cheapest to operate over the longer period of time, and kerosene or diesel will still have you running to the store often to try to keep up with fuel supply at random times, propane on the other hand is more precise and you can pick up a tank and know it will last you for this period of time, where with the liquid fuels they burn at different efficiency rates every hour depending on environmental conditions and such. Propane is known to be a "clean burning fuel" and that is also why the furnaces and CO2 generators used by the greenhouses around me also burn propane. Hope that helps.