In short, you don't want to use a temperature scale with an arbitrary starting point for doing calculations like this. The freezing point of water is no more or less arbitrary than the freezing point of oxygen or sodium or anything else. It's just one that's somewhat useful for everyday use. When handling calculations for multiplying temperature, you want an absolute scale like Kelvin.
Let's say the summer average is 30⁰C or 303.15 Kelvin
The absolute coldest possible temperature is -273.15⁰C, or 0K.
Halfway between absolute zero and 30⁰C/303.15K is somewhere around -121⁰C/152K
So if it were half as hot in the summer, it would be colder than ever recorded on earth.
In short, you don't want to use a temperature scale with an arbitrary starting point for doing calculations like this. The freezing point of water is no more or less arbitrary than the freezing point of oxygen or sodium or anything else. It's just one that's somewhat useful for everyday use. When handling calculations for multiplying temperature, you want an absolute scale like Kelvin.
Or Rankine if you're that kind of pervert.