Tempura is traditionally fried in vegetable oil blended with sesame oil. The sesame oil contributes a distinctive aroma and is associated with the traditional flavor and frying style of Japanese tempura.
Modern kitchens often use vegetable oil or canola oil on their own because these oils are widely available, relatively neutral in flavor, and practical for deep-frying. Specialty tempura restaurants may still use sesame oil or tea seed oil, sometimes in a blend that balances flavor, cost, and frying performance.
The type of sesame oil matters. Light sesame oil can be used for frying, while toasted sesame oil has a much stronger flavor and is generally better suited as a finishing or seasoning oil. The oil is only part of tempura’s texture: cold batter, minimal mixing, and brief frying also help create the characteristic pale, airy crust. Peanut, coconut, and olive oil are possible modern substitutions, but they are not the traditional pairing referenced by this question.