The models could be incomplete, or obsolete
Like, the intensity of current wars isn't even comparable to that of WW1 or WW2 battles.
The climate change can be expressed a the result of A+(B+C+D...) factors
Lets assume that A is some allegedly --hypothetical-- effect of the wars exploding bombs and releasing heat in the low atmosphere. If we claim that in World War II the value A was higher and nothing happened (So nothing will happen now), we are forgetting that the "everything else" part was much lower in WWII. Just the number of vehicles circulating was abysmally lower. This invalidates our guarantee, because all in ecology is relative to the current updated situation.
Ecosystems create buffers, the expect results are: not changes/very minor changes seen (buffer worked) or catastrophic change happens (buffer fell). Small amounts of energy released in one ecosystem could trigger noticeable effects in how the energy moves around the planet. As "how the energy moves around the planet" is too long, we created a shorter name for this: "Weather"