Before buying anything, go and find the most boring place in your home.
A ten degree daily swing on a kitchen counter is unusually bad, and there is nearly always somewhere much steadier a few metres away:
An unheated cupboard against an internal wall.
A basement or cellar, which in many houses is the most stable place in the building.
A north-facing room that is not heated.
A garage, seasonally.
Low down, since temperature stratifies and floor level is cooler and steadier than a counter.
Put a cheap thermometer with a minimum and maximum reading in two or three candidates for a week. You will usually find somewhere that varies by two or three degrees rather than ten, and that alone makes your results repeatable.
The other free lever is the amount of salt, for vegetable ferments. A slightly higher salt percentage slows things down, which partly compensates for a warm room, and a lower one speeds it up in a cold one. Not a substitute for temperature control and a genuine adjustment.
And for a starter specifically, the amount you keep and how often you feed it can be tuned to your kitchen - a smaller inoculation slows it, which is how people cope with warm summers without a fridge.