These are serious risks and real risks taken when using cheaply made appliances. From 2009 to 2013, U.S. fire departments responded to an average of 162,400 household fires that involved cooking equipment per year. The NFPA states that 40% of all house fires start in the kitchen (1). Safer equipment is installed with a number of fail-safe features to make for less accidents such as overheating shut offs. Internal thermostats monitor heating elements and automatically turn the element off if it has become too hot or is accidentally left on.
Start to familiarize yourself with qualification seals on product boxes and tags if you don’t already. Is the product UL certified? UL, or Underwriters Laboratories, is an American safety and consulting certification company. They are independent, not-for-profit and I wouldn’t trust a product that is not at least marked with the “UL certified” emblem. CQC and CCC are quality certifications for China that are often required for products manufactured overseas. The list goes on but what is important is that your appliances were tested and approved.
Sources: (1) http://www.nfpa.org/news-and-research/fire-statistics-and-reports/fire-statistics/fire-causes/appliances-and-equipment/cooking-equipment