Had I not already tried to do the same I would have said yes a broken fridge is fine. However been there and done that and I had problems. I think if I relate what happened to me this will show you the problems. The garage is integral so it has a temperature of zero to 28°C but the latter is short lived caused by sun on the tin door. My idea was the old fridge/freezer would allow me to move my brewing from the kitchen to the garage.
The temperature controller I bought was cheap, however I had made an error the MH1210A was same size as a STC-1000 but it could only heat or cool not heat and cool. i.e. one relay not two. So I built it into a box and plugged in a under floor demo heating tile, 18W this seemed ideal as heating from the bottom.
I tested the sensor, there was just 0.5°C difference between being in the brew and held tight onto side of fermenter under a sponge to insulate it from the air in the fridge. I used an energy meter to see how much power it used. And on the coldest day still average of 5W only so 18W was ample if not over kill.
I found my stick on thermometer was wrong, what I had not considered is to read the stick on it has no insulation so it shows some where between air and fermenter temperature, so I found 18°C was minimum temperature that fermentation would happen, so I would start the brew set at 18°C. In the first 24 hours the temperature would raise to 20°C maybe even 22°C and then drop again, this was with an ambient in garage of around 5°C. This was well within what I wanted and I was satisfied with results.
I found I needed to raise the temperature to around 21°C after first 5 days for the brew to complete within 21 days which I set as time I expected a brew to take. Once the first 5 days were over the brew would keep spot on temperature set.
However as Summer arrived I found 14°C ambient was the highest temperature I could start a brew at, over that and the fermenter would hit 24°C or over which was too hot. I tried to simply open the fridge door, but then it went too cold.
So since the fridge/freezer did work I bought a second controller this time a STC-1000 and set this one up to control the freezer compartment, I used an 8W bulb in the short draw and the fermenter was a tight fit in the lowest full size draw, had to remove air lock as not enough hight. The first day I tested it was really a hot day, the fermenter was at 22°C when it went in and the temperature set at 19.5°C the motor ran for 3/4 hour then stopped, by this point air temperature was 8°C in freezer and I expected it to over shoot, however as soon as the motor stopped the temperature started to raise again and after 1/2 hour motor cut in again for second time. Over the first 10 days the freezer used 0.10 kWh and never over shot, which was a contrast to heating which would regular over shoot.
After 10 days I move the fermenter from freezer to fridge, now in the cleaning stage I want a higher temperature and set at 21°C now the fermenting has nearly finished it will remain at 21°C even when the garage hit 28°C as the average temperature in garage is below 21°C even if it does peak to 28°C.
However the fridge/freezer is old, and will not last for ever, so I looked into other methods, the best seemed to be to use an old washing machine water valve and allow water to circulate when the temperature raises, but not really very good use of water and this summer my domestic water was hitting 18°C so it would need a lot of cooling water.
There are other methods but each one was a lot of messing about, and I quickly came to realise if my fridge/freezer fails, best option is get another fridge.
In the house the area is large, and with an ambient temperature in winter months of 19°C the brew works fine, without any heating or cooling, by June I would stop brewing and restart in September, although this year many got caught out with late hot spell.
So once the first 5 days have gone then the non cooled fridge will work fine, but the first 5 days you are likely to over shoot, so start in the house, then after 48 hours move to an old fridge will work fine. And in winter it will work fine anyway.
Clearly different brews want slightly different temperatures. Coopers will work hotter than most British kits, all down to yeast used, lager will need around 12°C and a fridge is a must.
But brewing does generate heat, so you must cool in first 48 hours and only warm after the first 48 hours, and it is that first 48 hours where the temperature is critical.
Once I got temperature control set up, I wondered how I ever brewed without it, I no longer need to check the s.g. although I do, but every brew is the same, they all take same time, so no longer do I need to monitor progress. Taken all the uncertainty away.
As a P.S. the fish tank heaters sit on the bottom. Never used one, but know many who do.
Be it a body warmer, cupboard, or fridge, you need control, and unless the fish tank heater is used then 95% use the STC-1000, the InkBird itc-308 is ready built and at £28 it is not really worth building your own any more. So if starting again I would get the itc-308 by Inkbird. By time you buy a box, and pair of sockets, the £7 for a STC-1000 soon hits the £28 mark with all the extras, so may as well get a ready built unit.