Philrob correctly states the general rule. One definite exception is that Norwegian Kveik yeasts. which are available in dry or liquid forms, ferment well at temps in the 30s. There has also been discussion on this forum about the tolerance of the yeasts in the Coopers kits. You can search for recent threads on both subjects on this forum.
Some form of temperature control would improve results, but you do not need to go out right away and buy the makings of a thermostat-controlled fridge. If your batches are in the range of 20L, you could start with a fridge that doesn't work as long as you have a good supply of blue ice from a good fridge and the patience to monitor temperatures. I did that for several years, and no, I did not get up in the middle of the night to check the beer. A RAPT pill would be an inexpensive way to monitor temps accurately.
Whatever you do, keep in mind that the early active stage of fermentation throws a lot of heat. That is when staying within the recommended range matters the most. If all that heat were retained, which wouldn't happen. fermenting to 5% abv would raise the temp by 30 degrees. So that is when you'd use blue ice or else run a working fridge frequently.
After those first three or so days, no great harm is done if the temp gets up into the 20s. If you stopped cooling your beer would be at about the daily mean temp. Variation is not good, but in an insulated environment like a fridge, you can put jugs of water in alongside the fermenter to add mass and help buffer temperature variation.
Or go all out and buy the works.
Ales are easier than lagers to get right, but if Queenslanders can enter Olympic bobsleigh races, they can brew lagers.
