I suggest you ask your contractor to come back and check it for your piece of mind. Wood will burst into flames at about 451 F - it is extremely unlikely the outside of your oven is anywhere near that hot. My guess is that the temperature of the outside is well below 200 F - otherwise you would not be able to keep your hand on it for 5 seconds. Your contractor should use either a IR thermometer , or better yet a contact thermometer to check the temperature of the case after the oven has been on an hour or so to make sure there is nothing wrong with the oven itself. I doubt you are missing a shield, but if you have the model number, you can go online and find the installation instructions and read them to see what they call for.

@Briana Bosch - since the wall has 3" of closed cell spray foam insulation, I believe it is forcing the water to flow down to the base. Nowhere is the wall wet. In fact, Im thinking of cutting off the drywall 1" away from the floor and put the vinyl baseboards, just to avoid getting the drywall wet.

If you go to fix it, please make sure after it is sanded, and you primer it, you use a small roller to put the stipple back, so it matches your plaster, or use the stiff end of a paint brush, to stipple it after brush painting, so it matches in.

Most likely the cracks are due to the house settling over the years. If house is on clay soil it may have dried out too much. Watering around the founation on regular basis will help eleminate the shifting of a house.