May one prepare coffee ingredients in a brewer such as this one on Friday and set the timer to brew the coffee for 8:00 Shabbos morning?
The Sefer Yerushas Pleita (Siman 16) brings from a sefer called Matta Yerushalayim that quotes in the name of the Chasam Sofer that it was common for people to set up a fire on Erev Shabbos in a way that would burn along a path until shabbos morning where it would reach the stove that had a coffee pot sitting on top and it would cook it.
Based off this the Shearim Metzuyanim Behalacha (Vol. 2. Siman 72 note 42) says that to set a timer for the coffee is not a problem. For although the electricity is lit on Shabbos, it is not any worse than the practice quoted above.
Of course the water and the coffee are already prepared in the pot before shabbos.
As noted in other answers here Rav Moshe Feinstein, as well as other prominent Poskim, forbade this practice.
This is not to be relied upon for practical halacha.
In a footnote in this document it states,
Iggerot Moshe, Orach Chaim 4:60. Rabbi Feinstein writes that use of timers to automatically regulate machines to perform work forbidden to Jews on Shabbat is generally forbidden, with the exception of turning lights on and off. He believes that use of timers would severely disrupt the Shabbat atmosphere, since all of one's work could be performed by machines. Rabbi Feinstein asserts that just as the Sages did not want, and therefore forbade, our asking non-Jews to perform work on our behalf on Shabbat for fear that this would disrupt the Shabbat atmosphere (see Rambam Hilchot Shabbat 6:1), so too the Sages would not want machines to do work on our behalf during Shabbat. Rabbi Feinstein appears to be the lone authority to adopt this approach.
It seems that if you want to follow Rabbi Feinstein then you should not set the timer to brew the coffee for 8:00 Shabbos morning.
In Rabbi Eider's Halachos of Shabbos page 322 footnote 657, he quotes a list of Rabbis who say this is assur. In order of his quoting them:
Rav Y. Henkin in Euros Yisroel page 122.
Tzitz Eliezer chelek 2 siman 6 & 7. Chelek three siman 18. Chelek 7 siman 16.
Minchas Yitzchok chelek 4 siman 26.
He mentions as well that according to some opinions placing the food on the heater erev shabbos and then having a gentile set the timer would be fine.
This was all mentioned besides Reb Moshe's opinion concerning timers mentioned in one of the other answers.
There was also a discussion in that footnote, from other rabbis as well, whether pre-cooked food can be placed on a timer before shabbos to simply reheat. Some allowed that, for instance Rav Henkin.
Shmiras Shabbos Kehilchasa chapter 1 siff 26 also seems to only allow pre cooked food to be placed on the cooking device erev shabbos to be reheated on shabbos.