My thinking has moved on to Myanmar or Laos now.
At that sort of latitude, including much of India south of the Himalayas, March (or April) to May (or June) is the Hot Season, when the humidity is high, the temperature is sky high, but it doesn't rain very much to cool you down. Generally reckoned to be the most unpleasant time of year in those parts. March will probs still be tolerable in the more northern parts of the zone, but April-May will be bad everywhere. The hottest month is April further south and May further north in the zone, before the monsoon breaks.
In NZ, March-May is clearly autumn. Probs still OK in the south in March, but you'll need to be working north. Still be reasonably pleasant in the far north in May - in fact March in Dunedin is about the same temperature as May in Auckland.
Pretty good time of year for Japan, (though perhaps autumn is the favourite) though make sure you aren't trying to take transport or book into hotels in tourist areas during specific spring holidays, as prices go sky high at those times. Spring happens pretty fast so you'll be cold in March and hot in May, and the rain will have started falling pretty heavily by May. Shouldn't be too expensive these days given what's happened to the A$ and JY over the past decade. Presumably much of China is analogous, though of course there will be gradations by latitude and altitude and interiorness.
