Laptop running hot

Alright, here's the situation... my laptop is running incredibly hot. I can't tell if it's an issue with the cooling fan or if the heat sink itself has given up the ghost.

Does anyone know what the damage looks like? How much are those replacements even going for these days?

A fan or a heatsink—they're technically different, sure, but they’re both working toward the same goal: keeping your hardware from melting. You probably have a fan that’s struggling, likely because air can't actually reach the components. This usually happens when you park a laptop on a soft surface like a bed without a stand, which basically chokes the airflow. Most of the time, you just take it to any local repair shop, tell them the thing is overheating and needs a deep clean, and the techs there will know exactly what's up. I'm betting the issue is just $33cleaning
.

Exactly. How old is your laptop? If it's an older model, there’s a good chance dust has built up on the heatsink, which kills the cooling efficiency. If that's the case, you should probably take it to a local repair shop to get it cleaned out. Usually, the fan starts getting noisy before it completely dies, but you can test it yourself—try blowing a little smoke near the vent to see if there's actually any airflow and how strong it is.

Also, make sure your vents aren't constantly blocked and that there's enough room underneath the laptop for air to circulate. You could pick up one of those cooling pads; they aren't expensive and they actually help. Even the cheapest ones will drop the temp by at least a degree or two.

But honestly, the most important thing is knowing if it's actually overheating. It's standard practice to install some free monitoring software to track temperatures so you can judge whether it's hitting dangerous levels based on the manufacturer's specs. Just feeling if it's hot to the touch isn't a reliable way to measure it. Plus, you have to factor in that it's been brutally hot lately; the ambient temperature is likely at least ten degrees higher than usual, which is definitely going to push your laptop's temps up...

Go ahead and get this program installed on your machine, then just drop a screenshot here for us to see.
http://www.cpuid.com/softwares/hwmonitor.html