I have a Hot Plate which is operated on a timer on Shabbat.
On Shabbat morning, while the Hot Plate is off, is it permissible to put
a) Dry food which has previously been cooked.
b) "Wet" food which has previously been cooked (i.e. some food with a gravy)
Also, does it make a difference Sefardi or Ashekenazi psak in this matter.
The laws of heating up food on Shabbat have become more complex, and interesting, since the advent of electrical heating trays (a Shabbat platter) and Shabbat timers which can turn them on and off at preset times.
In the situation where one has set the platter to turn on later, and one wants to put food on the platter before it turns on, there is some argument amongst the Rabbis. The work Shmirat Shabbat KeHilchatah (1,26) forbids placing any food on the platter on Shabbat even when the power is off, if it will turn on later. (Though this is partly because he forbids heating up cold fully cooked solids directly on the platter, as it looks like cooking. According to those who permit heating up fully cooked solids directly on the platter on Shabbat, putting them on the platter when it is off, and will turn on automatically later, is no worse than putting it there when the platter is turned on, and would be allowed. Alternatively, if one holds that they may heat up fully cooked solids on a lit platter by placing them on top of a dish or tray on the platter, they could do the same when the platter is off and will automatically turn on later). [He even forbids placing the foods on the platter uncooked before Shabbat, in order to be cooked when the platter turns on Shabbat.] This is the standard view that is held by most Rabbis.
However, in the works of Rav Ovadya Yosef shlitah, he writes that one may place even cold cooked soup on the platter on Shabbat before it turns on, so that it will automatically turn on later (Yalkut Yosef Kitzur Shulchan Aruch, 253.12, and Yabiah Omer, volume 10, Orach Haim 26). This is a minor opinion, but may be relied upon. Part of the reasoning to allow this is based on a question of "grama" or causative labor on Shabbat, which a simple reading of the Rema on the Shulchan Aruch forbids unless there is a real need. Because of this, I would not advise Ashkenazi Jews to rely on this lenient opinion unless there is a great need to do so (and where possible to speak to your Rabbi before doing so). Sephardic Jews rule more leniently on this question, and may rely on Rabbi Ovadya Yosef's ruling if they desire to do so - though many other Rabbis argue with it, and forbid putting food on the platter on Shabbat when it will turn on later.