Check File Mod Time On Page Load

functions.php

add_action('wp', 'test');
function test() {
  //get file modified time of style.css
  $time = filemtime('./style.css');
  $msg = "style.css was modified at: " . $time;
  $log_file = fopen(ABSPATH . '/theme_file_edit_logs.txt', 'a');
  fwrite($log_file, $msg);
  fclose($log_file);
}