> cold-blooded things like frogs have fairly massive genomes too
Yes, the genome size of the common frog (Rana temporaria) genome is 4.1 Gb. https://www.ncbi.nlm.nih.gov/datasets/taxonomy/8407/ which is larger than that of mammal genomes.
On the other hand, the smallest frog genome is the Ornate burrowing frog at 1.06 GB, which is 1/3rd the size of the human genome. https://en.wikipedia.org/wiki/Genome#Genome_size . https://en.wikipedia.org/wiki/Ornate_burrowing_frog says:
"This is an adaptation to the desert environment where it lives. Because the ponds where they breed dries up fast in the desert, the tadpoles has to go through metamorphosis as fast as possible, which can occur just eleven days after the eggs were fertilized. A small genome gives small cells, and the smaller the cells are, the faster the tadpoles transform into small frogs and can escape the shrinking ponds"
Xenopus laevis (African clawed frog) is 2.7 Gb, also smaller than humans - https://www.ncbi.nlm.nih.gov/datasets/taxonomy/8355/
Thus, warm/cold-blooded cannot be the main reason for the difference.
From https://en.wikipedia.org/wiki/Genome_size :
"genome size is not proportional to the number of genes present in the genome ... In eukaryotes (but not prokaryotes), genome size is not proportional to the number of genes present in the genome, an observation that was deemed wholly counter-intuitive before the discovery of non-coding DNA and which became known as the "C-value paradox" as a result."
From https://en.wikipedia.org/wiki/C-value#Variation_among_specie... :
"Variation in C-values bears no relationship to the complexity of the organism or the number of genes contained in its genome; for example, some single-celled protists have genomes much larger than that of humans. ... C-values correlate with a range of features at the cell and organism levels, including cell size, cell division rate, and, depending on the taxon, body size, metabolic rate, developmental rate, organ complexity, geographical distribution, or extinction risk ...