What seems to be the risk in using the API Ich treatment. Have read plenty of good things about it, can it really be so bad to couple with the heat treatment as well?
Colin answered directly, I would like to just add some general information as to why many medications can be dangerous, whether or not they may cure "x".
Fish continually "drink" water by assimilating it through their cells. Any substance dissolved in the water will pass into the fish, if the substance can diffuse across the cell membranes. The substance is then entering the bloodstream and being carried to the internal organs. Regardless of any thing else, this in itself can often be a risk to the fish. Medications should never be used unless they are the best treatment and are safe all else considered. This is why "treating" new fish that do not show any signs of disease, or assuming some disease and treating for that, is so risky; the harm to the fish can easily cause real problems because the stress from these substances is further weakening the fish, particularly its immune system, so it becomes more susceptible to disease issues which it would otherwise have easily handled.
There are very few fish we keep in our aquaria that will not be able to handle a temporary increase in temperature. During summer heat waves, the water temperature may well be higher than 30C/86F. Several years ago, my fish room would heat up to well over 90F/32C during a heat wave of several days, and the water temperature in the tanks obviously will match the air temperature; the air may cool at night, with the water cooling much slower, so over a period of several days the temp in the tanks remained very high. I never lost a fish. Increase surface disturbance to ensure a good exchange of oxygen/CO2, and most fish can easily manage the increase for this short a period (two weeks).
As others have mentioned here, mixing treatments is never a good idea, unless it is the best and safest course. There are very few example of this being safe or effective, but one is columnaris; using two antibiotics, furanizole and kanamycin, is very effective for this; but for most health issues, one treatment carried through is much safer than jumping from one to another.
As far as the "good things" about API of any other product...you cannot believe all you read. So-called "information" from unknown individuals on the internet is not a guarantee of accuracy or reliability.