I've no idea what movie this is but it sounds like the sort of intro you'd find in a giallo, and considering the ruckus PETA would make over burning a spider I doubt it'd be a U.S. production. Unless it's from the 70s. Films got away with a lot of crazy stuff back then.
Accordng to the IMDB there are a few movies titled Black Widow. This one: http://www.imdb.com/title/tt0090738/
has your espionage angle, but I don't recall anyone burning a spider in it. Then again it's been years since I've seen it.
Do you remember anything else about the movie?