Dell Inspirons have terrible placement of their cooling fans, IMO. (I have one too, which I inherited when its fan overheated and broke and was too expensive to repair...I repaired and upgraded, then inherited it...)
The fan is at the bottom, blowing air down (?!?). So if it's sitting on top of your lap (i.e. like a laptop...) often the fan is almost completely blocked by its contact with your lap.
It's a bad design. I'm quite surprised at how long it has remained that way. The only real solution that I know of is to prevent a snug fit between your lap, or any surface, especially soft one) and the underside of the computer. Prop it up on something so there is airflow to the fan vents onthe bottom.
Otherwise, as you've observed, it gets extremely hot. The next step is for the fan's motor to burn out. This is one of the most common failures for the Inspiron; it requires replacement of the fan. It's a cheap part, but repair involves taking almost everything out of the case to get at the fan. (An aside: this repair does take considerable time and patience, but it's an excellent one to do if you're interested in repair but not terribly experienced. It's not really that hard, just tedious, and the ifixit guide is excellent. And it's a great opportunity to upgrade just about anything in your laptop, since you'll be taking it out anyway. And you'll learn a lot.)
BUT. Prevention is much better. Anything that allows that air flow will do it. If the bottom of the laptop stays fairly cool, you're succeeding. A quick search at your favorite retailer for "cooling laptop stand" will reveal plenty of retail options. Or improvise something. Just be sure there's a grill or cutout or prop beneath that part of your laptop's underside--the part with the vent holes that gets too hot to touch if it sits on your lap. A small investment now will save you a major repair later.