Could an Erection Replace the Warmup

This might be way wrong, but I was thinking that when you have an erection, warm blood is flowing through the veins in your penis and it’s engorged. Would the blood flow be enough to sufficiently warm up the penis? Maybe an erection for a certain period of time, like 5 minutes (equivalent to hot wrap)? If this would work, it would be way easier than a wrap.

No, your blood temperature is 36 degrees C. The temperature of warm-up material (e.g. water in the shower) is greater than that.