Swift 3 version as extension:
extension FileManager {
    func clearTmpDirectory() {
        do {
            let tmpDirectory = try contentsOfDirectory(atPath: NSTemporaryDirectory())
            try tmpDirectory.forEach {[unowned self] file in
                let path = String.init(format: "%@%@", NSTemporaryDirectory(), file)
                try self.removeItem(atPath: path)
            }
        } catch {
            print(error)
        }
    }
}
Example of usage:
FileManager.default.clearTmpDirectory()
Thanks to Max Maier, Swift 2 version:
func clearTmpDirectory() {
    do {
        let tmpDirectory = try NSFileManager.defaultManager().contentsOfDirectoryAtPath(NSTemporaryDirectory())
        try tmpDirectory.forEach { file in
            let path = String.init(format: "%@%@", NSTemporaryDirectory(), file)
            try NSFileManager.defaultManager().removeItemAtPath(path)
        }
    } catch {
        print(error)
    }
}