How can I thoroughly test whether our ovens work? Emergency demolition of Kitchen right after we bought the house. 2 thermadours reinstalle

There's also a very simple. straightforward way to "heat map" your oven.

1. Get a loaf of sliced white bread - cheapest you can find - you want the slices uniform in size and thickness.
2. Line a baking sheet with them to cover it completely.
3. Put it in the oven on the middle rack and set the oven to 375'
4. Watch the bread as it toasts and browns. It will brown more quickly in your oven's "hot spots".
5. Remove the baking tray and take a photo of the baking sheet if you need to remember where the hot spots are.
6. Use the toasted bread for crumbs or croutons.

For instance - I know with absolute certainty that the back left corner of my oven is hotter than the rest, and therefor I need to rotate trays / pans / food halfway through their cooking time to ensure that they cook evenly and don't brown too much in one spot.

I want to thank everyone for their thoughtful answers. This is my first time using this website and I am delighted by the response to my question. Thank you all so much

I have had a Viking stove/oven for almost 20 yrs. Because it gets a LOT of use, parts periodically wear out. My Viking technician has a couple of fancy oven thermometers that he places near the top and bottom near the front, and I use my Taylor dial-type in the back. He sticks around a long time after he has installed/repaired to check (1) how long it takes to heat up to the different temperatures & (2) whether it actually stays at the desired temperature for several cycles of gas-on, gas-off. You may not have to take the thermometers out to check the temperature. You may be able to shine a flashlight through the window or crack the oven door and use the flashlight and the oven light to see. We generally check 350 and 450F. This method has worked well so far.
AntoniaJames' answer sounds very thorough. If you have a subscription to Cook's, they have tested and rated oven thermometers (or you can get a short-term on-line subscription to get the info on-line) and the top ones were inexpensive as well as reliable.
I think that hand-held laser thermometer sounds super cool if you have the space.

You can also buy a hand held laser themometer with a gun grip.. BonJour makes one model but I'm sure you can find others. Aim the beam at back floor and sides for a quick read.

I have no personal experience with this, or any particular expertise. Common sense would tell me, however, that I'd want to get three or four reliable thermometers. I'd put them in the various places in the oven. Then I'd preheat it, and check each of the thermometers once the oven told you it was ready. Then I'd put them back in and check them randomly, say, every twenty minutes, for a couple of hours. Then you'd know. I'd probably also check the manual for the ovens to see what they say. If you don't have hard copies, they are most likely online. Get the model number before searching for the manual(s). You should be able to print out a PDF, which you should do anyway, and read it from cover to cover, and keep it in your kitchen. If they're not online, call customer service and ask them to mail you one today. If the manuals don't have any info on this, I'd call customer service, ask for "Tech Support" and ask the staff what they think you should do. ;o)