import re

regex = r"\*{2}Header2\*{2}\s*([^*]+)\s*"

test_str = ("**Header1**   \n"
	"thing1  \n"
	"thing2  \n"
	"thing3  \n"
	"thing4 \n\n"
	"**Header2**  \n"
	"dsfgs  \n"
	"sdgsg  \n"
	"rrrrrr \n\n"
	"**Hello Dolly**  \n"
	"abider  \n"
	"abcder  \n"
	"ffffff")

print(re.search(regex, test_str).group(1))