FQ response is that it is not total bullshit. Resistant starches form in some foods with cooking and cooling even reheating, and they function similar to fiber. Some foods have more or less availability of their vitamins and minerals if cooked.
The opinion answer though is that if one’s overall pattern is diverse and healthy I have a hard time believing the differences matter meaningfully.
Is your question about differences due to the temperature immediately as/when eaten? Or about differences whether or not the food was cooked at some point in the upstream process?
Clinically significant effects of starch retrogradation (as seen when cooked pasta is refrigerated for a time before being reheated and eaten) may have been exaggerated. For instance, this review found that touted effects of appetite reduction and weight loss were not substantiated.
Anecdotally, I conserve uneaten portions of pasta in the fridge, later reheating and consuming them, and haven’t noticed any effect on satiety or communications from my gut microbiota.
Taste may be an underexplored benefit of chilling cooked pasta. Calvin Trillin once reported feeling nostalgic for packaged macaroni and cheese, being unimpressed after preparing it fresh, but noting that it was better when refrigerated and later reheated.
Not completely the same thing, but foods taste less salty when warmer. Or to put it another way: something that tastes perfectly seasoned will seem overly salty if you eat it cold the next day. So if you’re trying to limit sodium intake, you could potentially decrease the temperature served at.
Otherwise, lots of proteins can be denatured at certain temperatures or acidity, which may make certain nutrients more or less bioavailable to the consumer.
Learning to master fire was a major role in our evolution. When we learned to cook food the fire helped break the food down for us (requiring less work for our digestive systems), liberated calories that would normally pass through our digestive systems unabsorbed, and killed pathogens. This whole process allowed our teeth and jaw muscles to shrink, and gave us more calories, which helped our brains expand.
Aside from that, some vegetables lose their vitamins when cooked.
Vitamin C is destroyed by heat, but beta carotine in carrots becomes more bioavailable after cooking.
Resistant starch forms in cooked rice after it’s cooled for several hours. I have an older Chinese friend who was brought up believing that rice had to be served at every meal and had a really hard time when her doctor told her that she needed to cut down on rice because she was diabetic. Apparently the resistant starch in cooled and reheated rice made enough of a difference.