Can't comment on the kit.
Try and find a room or closest, ect that has the least amount of temperature swing. The closer you keep the beer to the ideal fermentation temperature range that the yeast you are using likes, the better.
I have a chest freezer with a temperature controller, but I mostly brew lagers now days. The easiest way if you're doing ales in the winter in a cold house is to buy a carboy heater and a temp controller so you can bring it up to ale temps. A basic inkbird controller and a carboy band heater can probably be had for under $60 if you look.
Can you make beer without that? Sure. But having some control over the fermentation process/temp goes a long way towards making a better and more consistent beer.
On the other side of that coin there are beers that are made in open fermenters with almost no control.