My laptop is an HP Envy. I played in beta for up to 12 hours in a row some days and had no troubles. I set the settings to maximum and went in and tweaked some things to help my performance a bit. Doing this, I had optimal quality with no extreme strain on my laptop aside from the temperature rising a bit high. If I was going to play for a long time I would prop my computer on an ice and make sure the fan vents were not blocked. I could do this because I have a wireless keyboard, mouse, and ps3 controller that I was using... My computer was just resting next to my TV connected through a HDMI cable. The ice pack thing is completely unnecessary, just an additional precaution for long term use ^^.
check out this guide: http://www.reddit.com/r/ffxiv/comments/1jkm9n/lunas_guide_to_optimizing_low_end_system_for_arr/
If you set the settings to max, then follow the tweaks you will get a score of ~2400. Which is "standard." Low to some people, but still.... when I played in beta, everything was beautiful, and I had 0 problems.
It uses Intel HD Graphics 4000.
OS Name Microsoft Windows 8
Version 6.2.9200 Build 9200
OS Manufacturer Microsoft Corporation
System Manufacturer Hewlett-Packard
System Model HP ENVY m4 Notebook PC
System Type x64-based PC
Processor Intel(R) Core(TM) i7-3632QM CPU @ 2.20GHz, 2201 Mhz, 4 Core(s), 8 Logical
Installed Physical Memory (RAM) 8.00 GB
I've highlighted some things that you may also want to look for in you laptop if you choose to go that route. These things will also make a difference in your game play. The graphics card isn't working solo to run this game for you ^^
Blah, I don't mean to sound rude... but I just don't believe you were running the game on max and having no issues with framerate and "optimal quality" with an Intel HD Graphics card. I have the same built-in HD 4000 card, as well as a Geforce 630M 2gb card in my laptop. When I tried running the beta, on lowest settings, with the Intel Card, I got about 4-6 FPS in heavily crowded places and topped out at about 20 FPS in places without a lot of people... on lowest settings. Swapping to my Geforce card was an instant and massive jump in FPS in all areas and overall performance. I also have the same i-7 processor and memory as you, so that's not the problem.
Also, you should never be putting your laptop on top of an icepack. They make specific cooling pads for them, but an ice pack on its own can cause condensation to get into your computer and completely ruin it.