As a detective, I start by analyzing the crossword clue itself. The term “oxymoronic” in the clue implies that the answer is a contradiction in terms. Pain relievers are typically associated with a cooling sensation, such as menthol or peppermint. However, the word “HOT” in the clue suggests that the answer may have a warming effect. After considering these details, I recall a popular topical pain reliever that provides both a cooling and warming sensation: ICYHOT. This product fits the criteria of the clue perfectly, as its name implies contradictory sensations. Therefore, I confidently fill in “ICYHOT” as the solution to this crossword clue. Solving this mystery was a fun challenge that required me to use my deductive reasoning skills and knowledge of popular products.