:welcome: Mcgannon
While this isn't really the most ideal place for this to be a first post, here's what I got...
I have been through a dozen or so older laptops and a handful of them have had cooling issues identical to this.
What I do is I disassemble the entire laptop and remove the CPU cooler. You can find a disassembly manual on google. The TIM (Thermal Interface Material) is usually a fabric pad coated with thermal compound. The pad is a pain to remove from the cooler without scratching the heatsink, but I use a product called ArctiClean (a specially formulated solvent for TIM) and q-tips. Once clean, I apply the thermal compound called "Arctic Silver 5", which uses microscopic silver flakes in a silicon paste which is non conductive (but messy) and has excellent thermal transfer properties. When I overclock I use this product and it helps to decrease CPU operating temperatures by 10 - 15 degrees F cooler compared to a standard thermal pad.
This not only helps to keep your lap cooler, but it also keeps under load temperatures lower due to quicker heat exchange between the CPU and the heat sink cooler. If you really want to make your lap comfortable, you can search for a tri-mount (three screws) 30mm fan that will fit the heatsink but with a higher RPM rating to evacuate the heat from the heatsink quicker.