The problem exists, because there is a check valve on the incoming line from the drill point in the ground. The water needs a place to expand. An expansion tank will take care of the problem, but I would also suggest checking the existing well expansion tank. Either the bladder is no good, or there is not enough room in the bladderless tank for air compression.
As water heats up, it expands, in a closed well system, it blows the p&t valve. An expansion tank absorbs the expansion.