Yup, it is that easy. I have already done what you describe recently not only to my own laptop and other systems I own, but for some of my clients as well. Because of how hot it gets here, I do a general system clean every month and a full on clean every year. On my laptop, I replaced the stock thermal paste with Thermal Grizzly’s Kryonaut. It helped a bit. Instead of the CPU getting to 90°C under full load, it tops out at 84°C. I will be replacing the fans in about another year or so. With the ambient temps I have, there is not much more I can do.