A dragon's gate sounds right up their alley, I like that idea.
And they also have the ability to use constant items such as heatstones or perhaps even a sort of light-focusing device to really get it handled. Yes, you can enter through the front gates... You're going to be dealt the damage of a blast furnace when you do

. Also could perhaps allow them to have an elemental bonus to protect them against their penalties. Fire Elementals summoned from within the Dragon's Gate to help protect their completely stone andiron fortress and burn the Hells out of paths through the forests?
The dwarves live on the mountainous side of a large island with a temperate climate and dense forests, they sit on top of the only known veins of an ore that makes casting spells difficult and throughout the area, but they have turned that into fine armour and weapons that resist magic.
So we're talking an almost Mediterranean climate. Ready forests for charcoal and coke, and plenty of wood for use in fortifications that can suffer in a 'scorched earth' policy.
They have a small amount of coal, a few volcanic hot springs, and an extensive seaport. So spells cast in the area near their mines, say within 5 miles of their main city, have to overcome a 20% failure rate and take 1 round/spell level to cast. Divine spells are slightly easier, with a 15% failure rate and a casting time of 1 round/2 spell levels. Magic items that do not need to be activated, like most weapons and armour, are not affected. Any item that needs to be triggered has a 10% failure rate. They have no immediate enemies at their gates, but spies and assassins from another city on the island are a problem and there are bandits and pirates to be dealt with. I may tweak these numbers, I'm open to suggestions...
Hot springs provide for geothermal energy to help keep them in a state of permanent spring even when the snows come and hurricanes. The mountains provide hidey-holes for them within their mines, to keep their University deep in the former mines. The Deep Scholars occasionally make noise with their inventions, but the rulers of the Land Above are fine with that because they provide for so many nifty inventions. They have learned to collect natural gas and purify it through use of their natural climate.
Their level of metalworking has allowed them to create waste processing facilities including
anaerobic lagoon processing. They have learned to 'bottle fire' in the form of this gas, which they learned to extract when a young dwarf set forth to learn the secrets of the 'killing vapors' deep in the earth. Using brass and glass that they created through mineral deposits and the smooth white sands of their beaches through dredging, the dwarf made the first 'ghost flames', and much of the city is powered or controlled through the ghost glass pipes that can be found throughout the area.
There is a natural gas processing plant within a mine shaft, kept under strict conditions. The pressurized gas is filtered using a three-step process of filtration through leech beds. This use of leech-bed filtration also inspired other filtration methods. The dwarven city has learned the power of clean water, and the production of charcoal-filtered spirits.
Yes, the dwarves have learned to make Jack Daniels during their evolution. They have also learned to create activated charcoal through their pressurization processing, and have been able to distill pure spirits for the use in cleansing. Most of their spirits are drawn from grapes and other fruits that come to use in their orchards and vineyards maintained through their use of viticulture and plant crossbreeding.
Oh, and due to their ability to perform pyrolysis they would be able to create simple biogas and biofuels, coke, and many of the chemicals which we have come to know and love for blowing stuff up. Stabilized nitroglycerin in form of dynamite and other explosives would be possible, and so many other things...
Really just depends on how far the rabbit hole goes for you personally. But definitely they could produce many fuels without the need for coal, natural gas, and other sources, and through the utilization of these methods could easily light the city, produce plants for heating, etc.
Slainte,
-Loonook.