The temperature here is higher than that in Tokyo.
ここの気温は東京（の気温）より高い
(ジーニアス英和第4版)
" I imagine that the climate there[in Southwold] is not so warm as that in Miami in the USA."
The climate in Miami is warmer than that in Southwold.
I suppose that it is not necessary to use ‘of’ after ‘not so … as that’.
I wonder if the expression ‘that of’ is a set phrase or not.
P.S.
添削で、thatの後にof を使う形に「チュータ」によって変えられる場合があり、そうしないとおかしいのかどうかと疑問に思っています。mustなのか、betterなのか、こういう言い方もあるなのかが、添削依頼者にわかるようなレポートがよいと思います。
Off the cuff in natural English, I would have said, “The temperature here is higher than in Tokyo”; “I imagine the climate there is not as warm as Miami, USA”, and “The climate in Miami is warmer than Southwold.”