They shouldn’t. High quality stop leaks are designed to be safe for all engine components. However, low quality versions used improperly are likely to damage your engine, so it’s important to get a high quality product and follow instructions very carefully. The type of engine may also matter - some engine designs simply aren’t as good for stop leaks, in which case an expert opinion might be helpful to learn more. Some people worry if a radiator stop leak can cause overheating, but this is rare for all high-quality formulas, some of which can even help cool your radiator.