generally the south side is warmer in the northern hemisphere.

...and/or thermometer.

Go outside at 1pm and whatever side is getting the full blazing sun then that's where you want to plant.

This is a hard question to answer. Is it winter warmth for plant protection from the cold or summer warmth that you want answers about? In winter the east side of the house is warmer in the morning because it starts to heat up while the west side is still experiencing its lows. So the low will be less long there. BUT the East side starts to cool off quicker so will reach the freeze earlier. This is true on the hill scale but I am unsure if this is markedly true on a house scale. This is very evident on west and east sides off a hill on a clear winter evening, but how that translates to the smaller scale of a house, I don't think will be as drastic. because it warms up faster in the morning so the low. If you have some masonry Thermal masses, they will keep things warmer. A winter covered stone patio facing south with large cement pillars is an amazing godsend in winter. Trees mess with this formula. I suggest getting a thermometer and walking it around and discovering your micro zones at highs and lows at different times of the year..

Not all houses have a true North south orientation. I had South east, south west, North west, Northeast. Northwest exposures are problematic because they stay in shade for much of the year and then get BLAZING hot western summer sun.

In summer, morning sun is cooler than western sun. All day southern sun is the longest exposure is the strongest. Start counting the hours of sunlight in your different areas. Trees mess with this.

We all kill plants learning. I still do. . Some famous gardeners , I know say that they don't conceder a plant in appropriate till they kill it three times.

Good luck.

Another thing to note is that slightly elevated areas will be warmer, since cold air drains into low-lying areas. But overall, the greatest effect is south-facing vs north-facing.