Option 1 states that cold-blooded animals have blood that remains cold all the time. This statement is incorrect. Cold-blooded animals, also known as ectothermic animals, have body temperatures that change in accordance with the temperature of their environment. Therefore, their blood temperature will also change accordingly.

Option 2 correctly states that the body temperature of cold-blooded animals changes in accordance with the atmosphere. This is a characteristic feature of cold-blooded animals, as they rely on external sources of heat, such as sunlight or warm surfaces, to regulate their body temperature.

Option 3 states that the body temperature of cold-blooded animals remains constant all the time. This statement is incorrect, as explained before.

Option 4 states that cold-blooded animals kill all the animals they come across. This statement is unrelated to the nature of cold-blooded animals and is incorrect.

Therefore, the correct answer is option 2.