Works with thermostat_live.ex:

import css from "../css/app.css";
import "phoenix_html"
import {LiveSocket, debug} from "phoenix_live_view"

let liveSocket = new LiveSocket("/live")
liveSocket.connect()

// grab time and weather temperature from thermostat
// --- assets/app.js --- vvv New vvv

document.addEventListener('phx:update', phxUpdateListener);

function phxUpdateListener(_event) {
  const time = extractTime()
  if (!time) {
    return
  }

  const temperature = extractTemperature()
  if (!temperature) {
    return
  }

  const message =  `${time}: ${temperature}`
  console.log(message)
}

function extractTime() {
  const timeSpan = document.querySelector('div.bar > span')
  return timeSpan && timeSpan.textContent
}

function extractTemperature() {
  const weatherForm = document.querySelector('span.weather form')
  if (!weatherForm) {
     return null
  }

  const result = /[+-]?\d+°[CF]/i.exec(weatherForm.lastChild.textContent)

  return result && result[0]
}

Certainly simpler than using a MutationObserver.

Thank you both. The phx:update event did the trick for us. Many thanks.

JS interop is an on-going effort.

So in case there isn’t a suggestion from anyone more familiar with LiveView forthcoming, it may be worthwhile to check out MutationObserver (as already suggested here) in order to run some client code in response to any changes in the DOM.