The HP Spectre 13 looks as luxurious as last year's model which was, for a while, the thinnest laptop in the world.

The latest version remains just as skinny at 10.4mm in thickness, which means its sides are too slim to accommodate even a USB Type-C port. Even more remarkably, HP has managed to equip the new Spectre with a touchscreen without increasing the thickness of the laptop.

Other improvements include a slimmer screen bezel, in line with the near-bezel-less trend seen in premium smartphones and laptops. With slim hinges supporting the lid, the Spectre's 1,920 x 1,080-pixel display almost pulls off the illusion of a screen floating in mid-air.

The copper accents that made last year's Spectre look either opulent or gaudy, depending on your taste, have been toned down. The result is an elegant, classy piece of high-end consumer electronics.

The keyboard is now more spacious as HP has moved the speaker grilles from the sides of the keyboard on the older Spectre to above the keyboard. As a result, it is more comfortable to type on, despite its shallowness.

The insides have also been upgraded. The processor is now the latest eighth-generation Intel Core i7 chip, which has four processing cores, up from two in last year's version. The amount of RAM has doubled from 8GB to 16GB.

In short, HP has done a good job of refining the Spectre's design and refreshing the hardware.

The new version is clearly better than its predecessor.

But the biggest flaw of the original Spectre remains. Because it is so slim, there is practically nothing, except for a thin layer of material, between your lap and the notebook's warm innards.

As a result, its bottom and rear get uncomfortably warm. They are noticeably warmer when the laptop is being charged through one of its three rear USB Type-C ports. On the bright side, the cooling fan in the new Spectre does not seem to be as loud as the previous version's.

The hardware upgrades have boosted the Spectre's system performance. It scores 3,262 in the PCMark 8 Home benchmark, which evaluates the laptop's performance with popular apps from Adobe and Microsoft. This is up from 2,594 for last year's model.

However, the new Spectre's slightly larger battery does not translate to significant improvements in battery life. It lasted around 61/2 hours in our video-loop battery test, which is about 10 minutes longer than its predecessor's stamina. But it falls short of other ultrabooks that have hit the seven-to eight-hour mark.

It is also slightly more expensive. My review set costs $2,899 compared with the $2,599 price tag for last year's Spectre.

•Verdict: HP's premium ultrabook gets even better with a touchscreen and system upgrades. But it still runs warm under certain conditions.