What should I write for unadvertised job

I graduated with a computer science degree & I'm currently studying master in data science (online uni) there is this research & Tech centre in my city that I've always wanted to work ( I dont know a lot about them but my dream is to work there) in their website they just asked to email about job inquiry I'm currently working as IT support at X company & I'm sick and tired of this job that is why I decided to continue my study hopping that I will get job as data analytic/science I have my cv & cover letter ready I have two questions 1) what should I write for the research/tech centre for unadvertised job 2) should I attack the cover letter or write it in the body if the email thank you

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