Students often assume that an academic essay must contain a lot of long words, and even use a thesaurus to convert the words they would normally choose into language which they mistakenly assume is going to be more impressive. This is a recipe for disaster, because a deliberate attempt to use difficult language for its own sake contradicts some of the basic expectations surrounding academic writing, especially the requirement to produce reader-orientated prose.
You should aim to write your essay as simply as possible, provided that you address the rhetorical situation surrounding your essay. Although you've probably come across plenty of academic writing you've found hard to understand, such writing is only difficult because it is attempting to engage with a complicated rhetorical situation. No critic has ever become widely read just because their writing was hard to read; there has to have been some motivation for the difficulty, some purpose which couldn't have been achieved in any other, for readers to feel that the struggle to understand them was worthwhile. As a student, you almost certainly don't know enough about the academic field to which your essay relates in order to achieve this satisfying kind of difficulty, so you should just try to write as simply as you can.
Using a thesaurus is a very bad idea, because a thesaurus does not give you literal equivalents of the word you first thought of, but only words meaning something roughly similar employed in a variety of very different contexts. There are no real synonyms in English (or in any other language), because for a word to remain in use at all, it must serve a different, perhaps more specialized, function than other words which resemble it semantically. All a thesaurus will do is to remind you of words which you could employ, but unless you are already very familiar with a word and the contexts to which it belongs, you will almost certainly not use the word appropriately, and this will just confuse your reader.