The points which, instantaneously, receive the least radiation during daylight hours must be (I assume) those that lie tangent to the Sun rays. These points rotate, so there's a whole circle of them surrounding each geographical pole. These points are not colder than the poles because (again, I assume) the radiation they receive is higher on average, although (instantaneously, during the day) the lowest anywhere on Earth.
So, the points on Earth that receive the least radiation on average must be within those circles. Which are they; are they the poles?
I should perhaps add that I am interested in the version of the problem that idealizes away from complications having to do with cloud cover or other atmospheric effects.