How is the hottest month in a calendar year dependent on the lattitude? Is it linear as in, if you go north from the equator the hottest time of the year moves out? Is it the opposite in the southern hemisphere? Why?
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The Earth tilts, and that tilt changes over the year. This means that the latitude where the sun is shining directly shifts over the course of the year. It goes from 23.5 degrees latitude in the North to 23.5 degrees latitude in the South. So the time of the year when your latitude is pointed directly at the sun is the time of the year when you are going to get the most solar energy, and your hottest day/month will come soon after.
It’s opposite in the Southern hemisphere, whatever month you are most pointed at the sun, June/July for the north. The closer you get to the equator the less change there is
I wouldn’t count latitude as one of the “important” causes for the lag of the seasons. The main contributor is the fact that the Earth, especially the oceans, are huge “warmth reservoirs”. Anywhere north of the Tropic of Cancer (23.4° N), the day of the summer solstice is the day where the sunlight is bringing in the most energy throughout the year. In the weeks following, however, the solar irradiation is still close to the maximum and still generally contributes to an increase in the “stored warmth”. Only some time later, when the reservoir has more energy in it and the sun has gotten noticeably weaker (lower on the horizon, fewer hours), the situation flips and the sun can’t bring in more stored warmth or even keep up compensating the “leaks” of the reservoir. This lag can be observed pretty much everywhere and is pretty much a worldwide occurrence. In the southern hemisphere it’s shifted by 6 months, in between the Tropics it’s a tad different, but that’s what the Earth’s tilt causes.
Now, there are several factors that determine how strong a specific area is subject to the seasonal lag. How close is a place to an ocean? Are there water or wind currents that amplify or weaken the effect? How is the climate there (is there typically a rainy summer, or droughts…). Are there usually large areas still covered by snow that reflect much of the sunlight until way into the summer?
Now, in regards to your specific question, I’m not aware of an obvious trend suggesting that higher latitudes have more seasonal lag, but I’ve never seen worldwide data. If you know of such a link, I can only speculate. Closer to the equator, the swing of amplitude of the sun’s height over the horizon is smaller –> the seasonal differences in daily hours of sun and in temperature between the seasons is smaller. Smaller differences in energy input would result in less time for the reservoir to catch up.
Because the Earth tilts, and so when the northern end of the planet is tipped towards the sun, that means the southern end is tipped away from the sun, and vice versa.”
In the Northern hemisphere July-Aug is the hottest months, and in the Southern hemisphere Jan-Feb is the hottest months.
It’s kind of hard to explain in words, but much easier [if you just see a picture of it.](https://spaceplace.nasa.gov/seasons/en/seasons.en.jpg)
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