I can't speak to the Hail Marys, but I can comment on how older recipes referred to cooking times and temperatures. In particular, there is a recipe book that was written or compiled by a man referred to as Apicius, sometime in the 4th century. Here is the link to the full list of translated recipies should you care to read them yourself. But in general, cooking time and temperatures are really not specified. Rather, Apicius frequently says that something "should be cooked until it is done." So there is an expectation that the cook be able to recognize when a particular item has cooked properly. Recipe 151, titled "Another Fish Dish, with Onions" from book 4 states,

"Another fish dish make as follows: clean any kind of fish and place it properly in a saucepan with shredded dry Ascalonian onions [shallots] or with any other kind of onions, the fish on top. Add stock and oil and cook. When done, put broiled bacon in the center, give it a dash of vinegar, sprinkle with finely chopped savory and garnish with the onions."

Sometimes he will make note of how the food should look or feel as a sign of doneness. Looking at book 3, recipe 82 titled "Cucumbers" the directions are as follows.

"Stew the peeled cucumbers either in broth or in a wine sauce; and you will find them to be tender and not causing indigestion."

As far as baking goes, I can really only speak to baking as it was in 18th century England and America. If you're looking for primary sources from this period, I recommend "The Frugal Housewife" by Susanna Carter. It can be found entierly digitized here. Baking recipes are included, but the standardized technique is as follows.

Temperature control was monitored in a few different ways. Just like if you were cooking over charcoal today, the optimal time to cook with a fire is when it has burnt down to hot coals and embers, and isn't giving off much in the way of flames. This is when the fire is the hottest, most stable, and burns the most efficiently.

So once the fire would be started in the oven, bakers would look for a reduction of flames and smoke. Once the fire was down to embers, the bakers would rake some of the coals out, close the door, and let the oven "soak" for several minutes. This was to ensure that the temperature in the oven became more uniform, otherwise there could be hot spots which could cause the bread to cook unevenly.

As a final test, the baker could throw some cornmeal into the oven and watch to see if it turned black or caught on fire, which would signify that the oven was too hot. When it came to the actual baking, it would be down to the baker to know when the bread was ready. The wonderful thing about old earthen ovens is that they hold their heat very well, so after a loaf or two of bread had been baked and the oven cooled slightly, they may cook other times like pies, pastries, beans, etc. with the residual heat. If this seems unscientific, that's because it was. Baking was a skill and a trade, which required apprenticeships and much practice before one became proficient with it. I hope this helped.