hotnessV0.js

class Post{
  constructor(){
    this.temp = Post.initTemp() // use large floating point number
    this.updatedAt = Math.round(new Date() / 1000) //unix timestamp
    //other init logic...
    //save object
  }
  hotness(){
    let timeInterval = Math.round(new Date() / 1000) - this.updatedAt // in seconds
    return this.temp * 2**(-1 * timeInterval / Post.halfLife())
  }

  upVote(){ 
    this.temp = this.hotness() + 1
    //save object
  }
  downVote(){
    this.temp = this.hotness() - 1
    //save object
  }

  static halfLife(){
    return 60 * 60 * 24 // simple 1 day half-life (score gets cut in half after one day)
  }
  static initTemp(){
    // this constant can be tweaked so that new posts appear in the desired location (probably half way down the page)
    return 5 // this means a new post is considered to be as hot as a post getting about 5 likes per day
  }
}

As for assembling hottest post, obviously you'd have to run the hotness function on the whole dataset, but i think a cron job that deletes everything that doesn't make the top 100 could take care of that for now.