A country everyone visits for the great galleries, and where the two rooms I think about afterwards are both private houses in Madrid.
Monday is the closing day here, not Tuesday, and the small houses keep shorter Sunday hours than the great galleries do. Check the afternoon closing before you plan an afternoon; the middle of the day is not a suggestion.
Both entries are in Madrid and ten minutes apart by taxi, which makes this the shortest country in the directory to walk and the easiest to underestimate. Give each of them a whole morning rather than halving one.
Winter is the right answer. The rooms are cool and empty, the light is low and flattering to old glass, and nobody is in front of the paintings. August I have never risked and do not intend to.