E.g. cold call in marketing, cold open in movies. Also "unsolicited" and "unexpected" seem to be synonyms but is there a better one?
2 Answers
Cold as in without thawing or warmth, originally in reference to unpleasant social relations (Old English), then expanded to meetings and other social (Mid. Eng.) and business (Mod. Eng.) interactions without introduction or affection. You also see the same sense in quit cold [turkey], meaning to stop without any preparation.
TvTropes calls a television "cold open" a teaser.
http://tvtropes.org/pmwiki/pmwiki.php/Main/TheTeaser
Also known as a Cold Opening or "Cold Open." A one to five minute mini-act at the beginning of the show, sometimes before the opening credits, that is used to set up the episode and catch the audience's attention.
. . . the first sketch right before the opening credits in sketch comedy shows like Saturday Night Live and MADtv is also called a cold opening.
The teaser has been used by many series since the 1950s. Today, nearly every American show has a teaser...Although the term is usually reserved for television, the practice is now prevalent in comic books, having crept into the medium in the mid-80s and grown popular through the 90s.
Some movies have an "Action Prologue" also known as a Bond Opening Sequence (from the James Bond movies); many now have a "cold open" before the title screens. http://tvtropes.org/pmwiki/pmwiki.php/Main/ActionPrologue?from=Main.BondOpeningSequence
The movie use of the teaser or cold open may be motivated by the distribution of movies first shown in theaters to the medium of television, where keeping the viewer's attention (preventing channel changing) is important.
"Cold calling" is well dealt with in the answer cited above.