Can one preserve food by periodically heating it?

YES! If food is quickly heated and kept above 140F/60C, microorganisms can't grow in the food. Professional kitchens use steam tables to keep food warm at this temperature throughout a day's service. If the product is cooled quickly (generally using an ice bath), then it can be used for more than one day.

Another approach is often used for stocks and soups: heat them to 165F/75C daily or every two days, to kill microorganisms, then cool them quickly with an ice bath to under 40F/5C. This can be done 2-3 times to extend the fridge life of the product.

The most important part of both approaches is to use a food thermometer to verify that food is fully heated/cooled, and to make sure that heating and cooling is done QUICKLY. For food safety, you do not want food to be in the 40F/5C to 140F/60C range for more than an hour if possible, or two hours tops.

Another trick to extend the fridge life of food is to immediately transfer it from a still-hot pot to a cool container, and then leave the top of the container open to allow steam to escape. This greatly reduces cooling time; even in a refrigerator, a sealed container may take over an hour to cool down to a safe temperature.

No.

Although it depends on what you call preserve.

Heating will kill off most of the bacteria that may have grown, but will destroy more and more nutrients each time you reheat. Also its important to reheat above 65C (maybe check that, its close to this figure).

For your sister, her pasta dish is perfect in the fridge for 2 days. In fact if she doesn't hav e fridge, its probably better to just leave it out than to reheat it every 6 hours. It wont grow anything dangerous in that time.

Different foods will provide different mediums for bacterial growth, some being more hazardous to leave in the danger zone (40f - 140f) than others. The method described might not be as great a risk for something acid as it would be for say, rice. But it should be taken into account that the heat used to kill bacteria will not necessarily denature the toxins that they excrete, so it strikes me that this sort of preservation strategy would become progressively more dangerous the longer you pursue it.

As people interested in cooking we should all be aware of food hygiene and take it very seriously. As such I would recommend against your sister's methods, they are quite dangerous.

While bacteria can't grow or reproduce at 60C many types are more than capable of surviving; their cellular processes will shut down placing them in a kind of stasis or hibernation. So in a restaurant freshly cooked food will stay bacteria free when kept at 60C, however that is not what your sister is doing.

The problem with these methods isn't the period when the food is hot, it's the period after its been heated as in practice it will stay warm for some time and this provides optimum conditions for bacterial growth.

Let's look at another piece of evidence, sterilisation. If one wanted to sterilise a babies bottle say it would not be enough to just place it in boiling water, instead it is boiled for some time. In fact a safer way is to use a machine which steams the bottle (steam can be far hotter). The only way to be sure something is totally sterilised is to autoclave it, this involves both steam and high pressure and the items are kept in these extreme conditions for some time. Ofcourse autoclaves are only used when one requires there to be 0 bacteria, say in a lab or hospital. The lesson: bacteria are hardy things which are particularly hard to kill.

Final remark, better safe than sorry, particularly when young children are involved.

This is useful information, true, but there is bacteria normally in food so it is not necessary or in one's best interest to injest food that is sterile and bacteria free. Heating is good preservatory measure but is not good when intended to be in use for long periods of time. ie: one can't plan to keep food preserved by constantly heating up for more than a day or two at most. Heat also denatures food especially protein so each time the food stuff is heated nutrients are lost, the food gradually looses it's freshness and original taste. In the long run, cooling is quite better.