I like little puzzles so I gave it a shot in Ruby.

  #!/usr/bin/ruby
  
  require 'digest'
  
  charmap = %w{zero one two three four five six seven eight nine a b c d e f}
  
  (0..0xf).map do |prefix|
    Process.fork do
      (0..0xffffff).each do |i|
        hex = "%01x%06x" % [prefix, i]  # "0123456"
        digit_words = hex.chars.map { |c| charmap[c.to_i(16)] }  # ["zero", "one", ...]
        sentence = "The SHA256 for this sentence begins with: %s, %s, %s, %s, %s, %s and %s." % digit_words
        sha = Digest::SHA256.hexdigest(sentence)
        if sha[0,7] == hex
          puts(sentence)
        end
      end
    end
  end
  
  Process.waitall

8 minutes on an old quad-core. I don't expect there's much to optimize since all the heavy lifting is in the libraries. I didn't bother with synchronization so you might get a scrambled result if it somehow finds a flurry of hits. :)