Just by reading your description, if I were you, I would not get it.
Simple layers of blanket (that lets air flow through) can just be covered over the cage if needed and during the winter and there are also so many other ways to keep your bird warm without spending too much.
I'd rather cover the cage with a few blankets than having to buy something where I'd put the cage and the bird inside like a trapped-confined looking container with a few air holes.
There are so many things that could go wrong.
What if the temperature heats up the inside of the cage too much?
What happens if it gets too cold or too hot?
What happens if the heater/thermostat malfunctions?
What happens if you're away or asleep and something happens to the temperature.
Do you know the material used for the heater and what kind of air is released?
What happens if there's not much breathable space? Yes, although there are air holes, (small ones compared to fresh and healthy air all around) the bird will be breathing in very warm air, unnatural and filtered air.. Just imagine being in a cage and then suddenly getting placed inside another big container with only a few air holes, breathing in the same, unnatural and warm/unhealthy air all day or just a few hours.
The bird could potentially develop breathing/air problems, can overheat, can't breathe properly or the lack of fresh air or any other health problems that you wouldn't normally get when you just have a cage outside.
The container can easily affect the breathing of the bird, and it will most definitely make the bird feel confined and possibly stressed out.
Rather than spending more money and since you say that the price is a problem, I'd stick with an easier, quicker and cheaper method which is to get a few blankets/bird safe heat warmers. You could if you wanted, get a hand warmer and place it nearby outside the cage where the bird cannot reach to it.
EDIT: I've looked further closely in the photos on the website and it seems like you can remove the front bit of the container? But even so, I wouldn't necessarily get it. Just simple blankets will do, unless, that's my opinion. Let's see what the others say.