At least once a week we get asked if The Brew Bag® will melt "if I need to fire up to get back to target mash temp". We always say, "without a false bottom in place, yes, and even then, perhaps." And then we provide a link to our blog post "Flame On...." and this post authored by Jake Huolihan and published by Brülosophy that tests the ability of brew dudes to distinguish between the same grain bill mashed at low and high mash temps.
The first article provides more detail about melting the bags and hopes to explain why we think flaming on to regain a few degrees is a waste of propane and creates opportunity for fire and a ruined beer, and the second provides substantiation based on taste test results that extreme mash temperature differences can not easily be detected in the final product.
So, to make our response more simple by allowing us to reference these two articles, and to allow this question to be searchable, we decided to write this blog entry.
The question that needs asking is "why would I need to maintain exact mash temperature?" The answer is based on a number of assumptions by most brewers, but ultimately, the answer is based on detectability by those consuming the beer.
Generally, the brewing community believes that different mash temps produce different tasting and mouthfeel results, and every award winning recipe published in the brew magazines provide a line item for the mash temperature and the time, so home brewers assume those factors are important to regard and should be followed - or the beer we make will be different than the beer that won the award. Also, pro breweries use systems that maintain an exact temperature so we also assume that since replication is important to their product offering, so it must be for us as well. However, equipment differences combined with the science of brewing tell a somewhat different story about what we should do, rather than assume. And there's a whole slew of award winning beers in home brew land that disregarded a few degrees in mash temperature, and yet, award winning they are.
1. Time to convert relative to temperature change.
At nearly any typical mash temperature, once the grain is added to the water, enzymes immediately begin converting starches to sugars. In rough measurements we've discovered that at fifteen minutes conversion is about 40% complete and by thirty minutes that percentage is ~75% to 85%. During that amount of time, even in an uninsulated vessel, the temperature loss will be 1.5º to 4º. So, even if exact mash temperature mattered, this loss has no impact on the types of sugars produced because the mash started in the targeted temperature "zone", and conversion is 75% complete .
So let's say that the remaining 25% converted at 5-7º less than the target temperature and now that wort is blended with the 75% that converted within 1º to 4º of the target, what then? The Exbeeriment confirms that experienced beer dudes can not consistently detect differences even at extreme mash temperature differences. So, blended wort with a conversion temperature of 75% at 150º and 25% at 145º - which is still in the Beta Amylase zone by a long shot - would certainly not be detected by anyone.
2. What happens when you flame on during the mash?
This is a repeat of the Flame On... post, but nonetheless - the wort at the bottom of the vessel superheats. Let me say that again with emphasis - superheats! Propane at the tip of the flame is about 3,600º. That temperature is being applied to the bottom of a metal kettle and although I can't provide any consistent data relative to heat transfer and size of kettle, type of metal, volume of grain and water, etc., I can tell you that the polyester bag will melt at 350º and sugar burns at the same temperature. And, the bag is sandwiched between the grain, which acts as an insulator, and the bottom of the kettle which is getting the full application of heat. Also, and this is critical - enzymes are already denaturing as time passes at proper mash temperature, and now we consider that denaturation is full on above 168º - so, attempting to raise the overall mash temp is killing enzymes and stopping conversion - the very thing we want to optimize. So why would we knowingly do this? And, for how long do you leave the flame on and at what temperature do you stop in order to raise the wort temperature to get the batch back to the target temp? Can you actually churn the wort from the superheated bottom to the top and back again to thoroughly mix the grain and the liquid, and what percentage of enzymes are sacrificed to achieve that?
Here's an excerpt from a Brew Your Own article written by Steve Parks -
"Beta amylase is active between 131° and 149° F. But like all enzymes, its activity reaches a peak, declines, and then drops precipitously as temperature increases. The rate is also dependent on the amount of enzyme present. It takes time for all of the enzyme to be destroyed, but what is still intact works very quickly. So as the mash temperature approaches 149° F, beta amylase is operating at its fastest rate but it is also being denatured.
This may seem trivial, but at these higher temperatures the denaturation is so rapid that the enzyme is mostly gone in less than 5 minutes. Also, in a home brewer’s mash tun, where the grain may be poured into very hot water, the exposure to very high heat for the few seconds before the mixture becomes homogenous may work to destroy the fragile enzymes."
By "high heat" he's referring to strike water temperature above 158º. You can read the entire article here.
Oh, and by the way, the hanging bag image used for the article header contains fifty pounds of grain - dry. Thanks Steve Thanos. He never flames on and has used the same bag many, many times. You could have found one of his award winning beers - Fifty Shades of Gorbachev's Birthmark on tap in Naperville, IL at Hopvine Brew Pub, but it's all gone. You can read his blog, Brewchive on Facebook.
Here's a few examples of superheating.
The bag below was in the mash tun full of grain and the user was stirring while the flame was on. No false bottom in place. So, yes, The Brew Bag® will melt if you flame on, but that's only one consideration when attempting to maintain exact mash temperature. 
Here's a burnt bag that was resting on a false bottom during the unnecessary mash out - too much confidence and not enough stirring resulted in a bad brew day. 
Another consideration is the bag that overhangs the kettle. Here's a photo of a nice clean separation that occurred during an attempt to get the mash back to target temperature. 
And here's one that could have caused a fire and a really big problem. 
Share the news - flaming on to maintain mash temperature is unnecessary, kills enzymes, and creates dangerous and costly situations.
Here's the Enzyme Temperature Range Chart. 
What about induction burners? Will they scorch a brew bag?