The most common and most likely answer to this crossword clue is the 4 letter word WASH
I've seen this crossword clue in The Guardian
W
A
S
H
More clues leading to the result WASH
Buddy explains!

The straight part
We know that "distemper" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case distemper = wash.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does WASH mean?
WASH noun- The process or an instance of washing or being washed by water or other liquid.
- A liquid used for washing.
- A lotion or other liquid with medicinal or hygienic properties.
- The quantity of clothes washed at a time.
- A smooth and translucent painting created using a paintbrush holding a large amount of solvent and a small amount of paint.
- The sound of breaking of the seas, e.g., on the shore.
- The wake of a moving ship.
- The turbulence left in the air by a moving airplane.
- Ground washed away to the sea or a river.
- A piece of ground washed by the action of water, or sometimes covered and sometimes left dry; the shallowest part of a river, or arm of the sea; also, a bog; a marsh.
- A shallow body of water.
- In arid and semi-arid regions, the normally dry bed of an intermittent or ephemeral stream; an arroyo or wadi.
- A situation in which losses and gains or advantages and disadvantages are equivalent; a situation in which there is no net change.
- A fictitious kind of sale of stock or other securities between parties of one interest, or by a broker who is both buyer and seller, and who minds his own interest rather than that of his clients.
- Waste liquid, the refuse of food, the collection from washed dishes, etc., from a kitchen, often used as food for pigs; pigwash.
- In distilling, the fermented wort before the spirit is extracted.
- A mixture of dunder, molasses, water, and scummings, used in the West Indies for distillation.
- A thin coat of paint or metal laid on anything for beauty or preservation.
- The blade of an oar.
- The backward current or disturbed water caused by the action of oars, or of a steamer's screw or paddles, etc.
- Ten strikes, or bushels, of oysters.
- The upper surface of a member or material when given a slope to shed water; hence, a structure or receptacle shaped so as to receive and carry off water.
- A lighting effect that fills a scene with a chosen colour.
- (stagecraft) A lighting fixture that can cast a wide beam of light to evenly fill an area with light, as opposed to a spotlight.
- To clean with water.
- To move or erode by the force of water in motion.
- To separate valuable material (such as gold) from worthless material by the action of flowing water.
- To clean oneself with water.
- To cover with water or any liquid; to wet; to fall on and moisten.
- To move with a lapping or swashing sound; to lap or splash.
- To be eroded or carried away by the action of water.
- To be cogent, convincing; to withstand critique.
- To bear without injury the operation of being washed.
- To be wasted or worn away by the action of water, as by a running or overflowing stream, or by the dashing of the sea; said of road, a beach, etc.
- To cover with a thin or watery coat of colour; to tint lightly and thinly.
- To overlay with a thin coat of metal.
- To cause dephosphorization of (molten pig iron) by adding substances containing iron oxide, and sometimes manganese oxide.
- To pass (a gas or gaseous mixture) through or over a liquid for the purpose of purifying it, especially by removing soluble constituents.