A box of Indian sweets is often kept on a shelf rather than in a refrigerator. Whether that is sound depends on how much water is left available inside the sweet.
Sugar ties up the water that microbes need
Microorganisms need water that is chemically free to move, not merely water that is present. Dissolved sugar binds a large share of it, leaving less for anything to grow in.
This is the same principle behind jams and candied fruit. A concentrated sugar solution is a hostile environment even though it is obviously wet to the touch.
The effect scales with concentration, so a sweet cooked to a thick, dense sugar mass is far more stable than one where the syrup has been left thin and watery.
Fat and roasting remove water as well
Sweets built on roasted flours and ghee are cooked until most of the water has driven off, which is why they set firm and crumble rather than staying soft.
Fat surrounding the particles also slows moisture from moving back in, so a well-made sweet resists the humidity that would otherwise soften it over several days.
Deep-fried sweets get the same treatment more abruptly. Frying drives water out at speed, and the crust that forms is a barrier against it returning.
Milk-based sweets are a different category
Fresh cheese and reduced milk sweets carry a great deal of water and a great deal of protein, which makes them a good growth medium rather than a poor one.
These are the ones shops keep in chilled cases, and they are the ones most likely to cause trouble if they are carried around in a warm car.
The visual cue is unreliable, since a milk sweet can look and smell fine well after it should have been discarded. Time and temperature matter more than appearance.
Humidity is the variable that undoes storage
Sugar is hygroscopic, meaning it draws water from the air. A sweet left open in a humid kitchen slowly picks up moisture and loses the stability it was made with.
Once enough water has been absorbed, the surface turns tacky and the protection weakens. Airtight containers matter more for shelf-stable sweets than for anything kept cold.
Air conditioning cuts both ways in an American home, drying the air in summer while winter heating can leave a kitchen swinging widely in humidity across a day.
Judgment should follow published guidance
Food safety agencies publish clear advice on holding times and temperatures for dairy-containing foods, and that guidance is a better basis than the practice of a home kitchen elsewhere.
The general rule that follows from the mechanism is simple enough: the drier and sweeter the item, the longer it holds, and anything soft and milky belongs in the refrigerator.
Bought sweets carry another unknown, since a shop's own handling before the box reached you is not visible. Buying from a busy counter with high turnover reduces that uncertainty.