Mammals have the smallest and most flexible blood cells of all vertebrates, which are made inside the mammals bones. It allows for miniature capillaries, and perhaps different sensory abilities.
Dinosaur blood cells could divide, they kept their nucleus, and were larger, and so they could have different bone structures, perhaps stronger and lighter.
Mammal bone structure may be limited by the marrow, which doesn't exist in birds and dinosaurs.
Most current research suggests that Dinosaurs, the most recent family of giant lizards, were not cold blooded. Scientists use terms like Archosaurs, to describe all large lizards. The older lizards had temperature regulation like crocodiles, and the later ones had feathers and warm blood. They can measure isotopes from teeth and bones to determine ambient temperature at time of growth, which were about 35.7>t'>38.2 in dinosaurs, warmer than crocodiles (30) and colder than birds (38) https://blog.everythingdinosaur.co.uk/blog/_archives/2011/06/20/4845668.html
You are focusing on only one factor, to say why they couldn't co-exist. Mammals were in a nocturnal ecosystem niche and only small advantages in one group of animals provides enough pressure to prevent the other group from becoming the same size and competing with them.
Other advantages can be: Faster growth rate, bipedalism(dino's had either 2 fast legs or armor/size), full body armor protection(elephants are jelly for velociraptors), live-bearing versus egg laying(pregnant and young mammals), neurological(some dino's had secondary brains in the spine), skeletal(bone marrow vs hollow bones), muscular and other factors that tailored dinosaurs to speed strength and efficiency at large sizes. Dinosaurs did live in cold forests, and the best boreal megafauna are like balls of blubber with little legs compared to dinosaurs, feathers are better protection than fat.
The reason why birds did could not return into the ocean and become masters of the seas like whales, is because they would have to lay eggs in the sea which even penguins and marine birds haven't evolved.
There were warm blooded sea-swimming dinosaurs (mososaurs) that looked like diplodocus which gave birth to live young at sea, so birds like penguins and gannets are fairly close to becoming whales again given time.