Question:I cook rice in the microwave. On Shabbat, I want to heat it up on the hotplate. Besides the regular questions of reheating, is there a problem because the first cooking was irregular?

Answer:We will begin by looking at a precedent regarding non-standard cooking. The gemara (Shabbat 39a) says that it is permitted to "cook" a food in the sun on Shabbat. The prohibition of cooking is when something is cooked by heat that emanates from some sort of fire (Shabbat ibid.). Rashi (Shabbat 39a) says that the leniency is because it is not normal to cook in the sun. The Igrot Moshe (Orach Chayim III:52) says that because of the abnormality, we cannot extend the prohibition from the cases of cooking in the Mishkan, which are the model for what is forbidden. Others disagree, based on another gemara (Pesachim 41a), which says that just as there is no Torah level violation of Shabbat to cook meat not through fire or its by-product (e.g., hot springs) so there is no prohibition of eating Korban Pesach meat that was so cooked. Since it is the result, not the process that is important regarding Korban Pesach, the Avnei Nezer (OC 163) and Minchat Shlomo (I, p. 105) say that Chazal must have posited that the unusual process produces a result that is different from standard cooked food.
The Pri Megadim (OC, Mishbetzot Zahav 318:6) briefly discusses whether it is permitted to put something that has been cooked in the sun through a conventional cooking process on Shabbat. His context is the machloket of the Rishonim on whether it is forbidden to cook (in liquid) on Shabbat something that was baked (dry) before or vice versa. We rule stringently but not conclusively (see Shulchan Aruch, OC 318:5; Shemirat Shabbat K’hilchata 1:(180)). The Pri Megadim’s case has elements of both stringency and leniency in comparison. On one hand, there the food already underwent a halachic cooking, whereas here it has not. On the other hand, cooking something baked and vice versa makes a discernable change, which might not be the case when repeating basically the same process in a "halachic manner." The Pri Megadim’s leaning is that there is certainly not a Torah violation and it is likely permitted, apparently based on the idea that the cooking process is (fully) forbidden only when it changes and/or improves the food (see Rambam, Shabbat 9:3).
If we equate microwave cooking to cooking in the sun, your question is equivalent to the Pri Megadim’s. However, that equation deserves evaluation. With the advent of microwaves, the question arose whether it is as a new-fangled but essentially standard form of cooking or whether it is a new application of Chazal’s non-halachic fireless cooking. (Problems of the use of electricity basically preclude the use of a microwave on Shabbat in any case.) The Igrot Moshe (ibid.) claims that since microwave cooking is now a normal form of cooking, it is derivable from the Mishkan. While the context of his ruling was to be stringent (not to cook), which is easier to do than to rule leniently (see Rashi, Beitza 2b), he probably considers microwaving to be cooking regarding the halacha that there is no problem of cooking thereafter. In fact, all might agree that the results of microwaving are more similar to regular cooking than cooking in the sun is and permit reheating such food with a standard heat source.
Some people like rice crispy, and the relatively high heat of many of today’s hotplates can accomplish that. Doing so is a problem even for normally cooked rice, as this is a significant act of baking after cooking (see Shemirat Shabbat K’hilchata 1:60). If one makes sure it will not become crispy, that should suffice for our case as well.
If one wants to be stringent (see uncertainty in Tzitz Eliezer X:62; Yalkut Yosef 318:(19)), he can bake the rice in a regular oven after taking it out of the microwave, to make sure it is halachically cooked before Shabbat (see Be’ur Halacha to 318:5). Five minutes, a nominal cooking process, should suffice. If one likes the rice crispy, this should be done on Friday (see Shemirat Shabbat K’hilchata 1:71).