Q.Growing a tree in a pot
I have bought a Flowering Cherry Tree (Prunus Hanagasa) as a 2 year old tree in a container. I was planning to transfer it to a larger pot and leave it there for a year or possibly more, as we need to re-model the garden. Reading the article above has made me worried about the risk of the roots being affected by frost and heat. Is this tree likely to be suitable for a pot?

Trees in pots are affected by the temperature more than those in the ground, but your Prunus should still be able to survive because most are hardy down to gardening zone 5 or lower, while you are probably in zone 7 or 8. Providing winter protection around the pot can help, as described in the below articles. To avoid heat stress, don't use a black colored pot.
https://www.gardeningknowhow.com/plant-problems/environmental/protecting-plants-winter.htm
https://www.gardeningknowhow.com/garden-how-to/info/wrapping-plants-in-burlap.htm