Monarch butterflies can fly only with a body temperature of at least 55.0   degrees  

Choice B is correct. It's given that monarch butterflies can fly only with a body temperature of at least $55.0 \text{degrees} \text{Fahrenheit} \left(°\text{F}\right)$. Let $x$ represent the minimum increase needed in the monarch butterfly's body temperature to fly. If the monarch butterfly's body temperature is $51.3°\text{F}$, the inequality $51.3+x\ge 55.0$ represents this situation. Subtracting $51.3$ from both sides of this inequality yields $x\ge 3.7$. Therefore, if the monarch butterfly's body temperature is $51.3°\text{F}$, the minimum increase needed in its body temperature, in $°\text{F}$, so that it can fly is $3.7$.

Choice A is incorrect. This is the minimum increase needed in body temperature if the monarch butterfly's body temperature is $\text{53.7}°\text{F}$, not $51.3°\text{F}$.

Choice C is incorrect. This is the minimum increase needed in body temperature if the monarch butterfly's body temperature is $50.0°\text{F}$, not $51.3°\text{F}$.

Choice D is incorrect. This is the minimum increase needed in body temperature if the monarch butterfly's body temperature is $48.7°\text{F}$, not $51.3°\text{F}$.