Handy Sitecore.Contex is thread-local storage, so as soon as leave you leave sweet and warm asp.net request thread, you need to set it up for yourself. Fortunately, it is an easy task: you should pass a Sitecore site name to your child thread  (available as Sitecore.Site.Name in the parent thread if you want to execute in the same site context), and then do a Sitecore.Context.SetActiveSite(aSiteName).

Optionally you might choose to either switch the security checks off
  Sitecore.Context.Security.EnterState(SecurityState.Disabled)
or leave the security intact, pass a user name or id to your thread and do a
  UserItem user = Sitecore.Context.Domain.GetUser(aUserName);
 Sitecore.Context.Security.EnterUser(user);

Sites are setup in <sites> section of the web.config file, so if you want your thread to execute in specific context with its own settings (own database, perhaps) - set up another site in web.config and use its name instead.

Setting up context when you spawn a new thread is rather important - even if you don't use it directly, most of the higher-level API does.