When it comes to the topic of mold it is truly something I have spent a lot of time learning a lot of things about and have a lot of years of experience with on a personal level. First of all mold stops growing completely at an RH of 30% and anything lower than 30% allows that mold to become a dry powder which can and will float in the air for great distances. That is why when cleaning mold, the first thing you want to do is to saturate it with a liquid, depending on the surface I'll use bleach, vinegar (white vinegar when it comes to surfaces and AC vinegar when it comes to plants) or a product I buy which can found at big box stores called "Mold Armor" which comes in a spray bottle as well as a house wash and prevents mold as well as kills mold on household surfaces. As it was already pointed out there is a number of different types of molds, and they are constantly around in the air all the time just waiting to find food and water in which to take off and grow. Once you pass around 60-70% RH molds really have all the moisture they need to get going really good, and in a greenhouse type of environment that is the perfect conditions for molds to take off in.
You stated the mold was on a heat mat, which doesn't surprise me because the heat mat would help to condensate any moisture in the air between your pot and the mat making it a perfect spot for the mold to grow, the heat mat then dried out the water which condensed there and thus dried out the mold. If it were me, I'd just wipe everything down with a bleach water or vinegar water wash and dry it with a dry cloth and give the pot a little air circulation underneath it to prevent future issues. I like to keep 1/4 of an inch or a couple of coins under the pots to prevent condensation building up between the pots and the surface they sit on, it also allows any spilled water to evaporate that may not get wiped up.
Another thing which caught my eye was that you water your plants everyday, and yet you do not think you overwater them, which I am sorry to say is wrong because you are over watering them. The soil needs to be soaked with water and then allowed to dry up completely before watering it again. When you water just a little bit every day, what you are doing is you are just getting water to sit in the same places in the soil every time because of the way water flows through the soil, as it will always take the path of least resistance. This leads to wet pockets of soil which in turn become havens for anaerobic bacteria, fungus, algae, etc... to begin to have a great breeding ground for, and you will think you are doing so good and then suddenly one day your plant will droop and you won't know why, and by the time you figure out your soil smells sour or like raw sewage it will be to late to do anything to save the plant. You don't even have to take my word for this, you can look it up on a search to see I'm completely serious on this.
When you say "peroxide" I am assuming here you are meaning "hydrogen peroxide" 3% drug store over the counter strength? I am not sure the strength you are using by the time its mixed with the water, but it shouldn't be more than 10% at maximum and even then I would strongly recommend you go and do a lot more research on how to use H2O2 (hydrogen peroxide) correctly when it comes to using it with your nute water to water the plants. H2O2 is great for cleaning because it eats organic material, and that is why when I did my own research on this I found that some information out there brought up the need to let the H2O2 water sit for a period of time prior to using it, so it is not so damaging to the tender young roots of your plants.
The other thing I wanted to touch on was the temp of your root zone, you may not realize this but the temp of your root zone is very important the same as it is for hydro growers, you want a root zone temp around 68-degrees, once you move past 72-degrees you are making the water hard to hold oxygen and believe it or not roots need oxygen to be healthy and to survive. Once you pass 75-80 degrees water holds no oxygen anymore and that is where you get stagnant water and the smells of sour or sewage from the water or soil. If the plant canopy temps were cooler than you wanted them to be, then you can raise the root zone temps to compensate to prevent stressing the plants. If the plant canopy temps were to be 90+ and you couldn't get the temps down, then someone could even lower the root zone temps to 60-degrees to prevent stressing the plants I've read with great success. The closer you keep your root temps to 65-degrees I do know will greatly increase how much your plants can take up for nutes, even if you oxygenate your root zone even with some 1/4-inch soaker hose and connect it to a fish aquarium pump in a soil grow. No, I am not kidding, I wondered this for years and then a couple years ago I saw the AD in a magazine for this basic concept being marketed by someone and it won all kinds of awards because this idea and concept really does work, will help the plant to uptake even more nutes and grow faster yet.
