Other than very low-powered systems, laptops have not been laptops for many years now. 

Air intake on the bottom is normal for many laptop models and brands, so what you describe is the opposite of unusual.

Heat and ventilation are issues with pretty well all modern thin laptops. Always use the laptop on a hard surface, never on a bed, couch, pillow, etc. Heat can shorten the life of components, so do what you can to assist its cooling.

You might want to do what I did:

I took a strip of lumber, about 3.5 cm. wide x 2 cm. high (1.5" x 3/4"}, and the length equal to the width of my laptop. I routed out two notches to accommodate the laptop's rear feet. The rear of the laptop sits in those notches, propping up the rear by 2 cm. That provides better ventilation underneath the laptop and makes it easier for the fan to draw in air via the bottom vent. 

It's cheap insurance, and also positions the keyboard at a slight angle that makes typing more comfortable. It won't solve a major heat issue, but it helps somewhat.

You can also reduce heat caused by Turbo Boost by changing power settings.
Settings | System | Power & Sleep | Additional power settings | select your plan | Change plan settings | Change advanced power settings | Processor power management | Maximum processor state: set to 99% or lower.
If you set it to anything below 100%, Turbo Boost will not activate, so system will not generate as much heat and you will save battery power.

And in that same panel, make sure System cooling policy is set to Active.

In some systems, Turbo Boost can be enabled/disabled in BIOS/Setup.

If you are experiencing cooling issues with your Dell Precision Mobile 3470 laptop, it's essential to address them promptly to prevent potential hardware damage and performance problems. Here are some steps you can take to troubleshoot and resolve cooling issues providing by currentpackages:

1. Check for Dust and Blockages:
Over time, dust and debris can accumulate inside the laptop's cooling system, hindering airflow and causing overheating. Turn off your laptop, unplug it, and remove the battery if possible. Then, use compressed air or a soft brush to gently clean the air vents and cooling fan. Be cautious not to damage any internal components during the cleaning process.

2. Verify Power Settings:
Ensure that your laptop is set to the appropriate power settings. Go to "Control Panel" > "Power Options" and select a balanced power plan or any power plan that allows your laptop to manage its cooling properly.

3. Update Device Drivers and BIOS:
Make sure your laptop has the latest drivers and BIOS version installed. Visit Dell's official support website, enter your laptop's service tag or model number, and download the latest updates for drivers and BIOS.

4. Check Task Manager for Resource-Intensive Processes:
Open the Task Manager (press Ctrl + Shift + Esc or right-click the taskbar and select "Task Manager") and check for any resource-intensive processes that might be running in the background and causing the laptop to overheat. End or close any unnecessary tasks.

5. Elevate the Laptop and Use Cooling Pads:
Elevate the rear of the laptop to improve airflow by using a cooling pad or placing the laptop on a flat, hard surface. This helps in dissipating heat more efficiently.

6. Avoid Using the Laptop on Soft Surfaces:
Using the laptop on soft surfaces like beds or couches can block the air vents, leading to inadequate cooling. Always use the laptop on a hard and flat surface.

7. Reduce Performance and Graphics Settings:
If you're running graphics-intensive applications or games, consider lowering the graphics settings to reduce the strain on the GPU and CPU, thus generating less heat.

8. Check the Fan Operation:
Listen for the cooling fan's operation while the laptop is running. If you don't hear the fan spinning or if it's making unusual noises, there might be a hardware issue with the fan, and you should contact Dell support for further assistance.

If the cooling issues persist after trying these steps, and your laptop is still overheating or shutting down unexpectedly, it's recommended to contact Dell support or take the laptop to an authorized service center for a thorough inspection and possible repair.