An electronic tool for mixing while the pot is on the fire
For thick sauces and puddings, I would think an immersion blender is the way to go. Some even have removable shafts, so you can change the length of stick attachment to fit your pot, or switch it out for different accessories, like a whisk attachment. And at risk of sounding like an infomercial, they even sell bowl clamps for hands free operation!

Me personally, I like a drill and mixer attachment.