Combine tuna, cream cheese, oil, lemon juice and cayenne in a food processor and process until smooth. Transfer to a serving bowl; stir in capers, parsley and thyme.
Make Ahead Tip: Cover and refrigerate for up to 2 days.
Note: Chunk light tuna, which comes from the smaller skipjack or yellowfin, has less mercury than canned white albacore tuna. The FDA/EPA advises that women who are or might become pregnant, nursing mothers and young children consume no more than 6 ounces of albacore a week; up to 12 ounces of canned light tuna is considered safe.