May a person set a coffee pot on a timer before Shabbat to make coffee for Shabbat morning? If this presents a problem of Bishul, then can a person set a coffee pot on a timer to make coffee for a Yom Tov morning? And, are either of the above two questions handled differently if the coffee maker is the type that both grinds the beans and makes the coffee automatically (as opposed to the "standard" machine which uses preground beans)?
It is not permitted to brew coffee on Shabbat using a timer. Although you would not be violating Shabbat thru “Bishul” since everything is automatic, there is a rabbinical injunction against leaving uncooked food on a fire over Shabbat [=”sh’hiya”] (Chazon Ish Orach Chayyim 38 2; for a fuller discussion of the question see Shemirat Shabbat KeHilchata I 26 n. 73 and the sources quoted there). On Yom Tov this injunction does not apply. One may use the coffee- maker on Yom Tov even if it grinds the beans but only if the use of a timer to delay grinding the beans is commonplace. Otherwise the noise of the grinding would cause someone who heard it to believe that you turned on the electric grinder on Yom Tov (see Rema Orach Chayyim 252 5; Shu”t Tzitz Eliezer IV 31).