Home made pickled peppers without sodium - botulism risk?

As Lorel C mentioned in the comments, botulinum clostridium won't grow in acidic environments. It also won't grow in cold environments. You've got the peppers in vinegar and in the refrigerator. I think you're good.

Even with the peppers being fairly warm when refrigerated— it's always a good idea to let things cool in the open air before putting them into sealed containers in the refrigerator because even under refrigeration they'll take much longer to cool in a sealed container— adding a bunch of acid and storing the jar in the refrigerator reduces the risk to pretty much nothing.

You primarily have to worry about botulism when you've got things in an anaerobic environment (e.g. covered in oil, or honey, or vacuum sealed, or in a package filled with some other sort of gas, or packed into sausage casings) between 3C/37F and 50C/122F, with a PH above 4.6. Garlic and onions are more likely to have spores on them because the spores are very common in the soil of many places where garlic and onions are grown.

In the famous case where a man was poisoned with botulism toxin when eating a home-pickled egg, they determined the source of contamination was a toothpick which he used to poke a hole in the eggs— a commonly-used (and likely ineffective) method to get the brine to penetrate pickled eggs more thoroughly. The spores entered the egg via the toothpick, the hole in the egg was an anaerobic environment suitable for the bacteria to grow, and he stored them at room temperature. Had he simply stored them in the refrigerator, the spores would have remained dormant, he could have eaten his tasty eggs, and he would have been alive to tell us how tasty they were.

If you want to nerd out on this for a hot second, here is an article that discusses bacterial growth as it relates to food production and storage.

In general, with pickled items we can many of them to make them shelf stable, not so much to kill the botulism. There may be a few things that the heating adds some additional security with, like if the final Ph was a bit higher than intended, but mostly the vinegar does the job as long as you are getting it to the right levels.

Now, next question is, how long are they then safe for under refrigeration? This article https://www.eatbydate.com/other/condiments/how-long-do-pickles-last/ seems consistent with others I could find. It is referring more to commercial product after opening, but home made to proper standards I would think would be similar. They state that refrigerator life after opening, with proper storage, is similar to original shelf life of canned, 1-2 years beyond commercial "best by" date. Now, yours are home made, so you did not open them and don't have some best by date, but I think it would be safe to say treat them as an opened item which has already reached its best by date and error to the low side. If you like them, use them within a year. If you do not use them within a year, meh, must not have turned out the way you wanted, so toss them and try again.

What is proper storage? There might be a could points I am missing, but generally, make sure they are not contaminated by other items. Make sure the item stays fully covered by pickling solution. Make sure lid is in place and clean when putting back in the refrigerator. I would discourage removing product and then putting left overs back into solution. Such things might not be high risk, but do introduce some risk in contamination and defeating your pickling protection, and will deteriorate quality even if they do not cause illness. The pickling solution can only protect if the product is in it though.