The gas, oil and temp gauges DOES work on heat. I did an effort to repair my temp and oil gauges many years ago. Took them all apart.
On modern gauges there is a coil that moves in a magnetic field. Less resistance from the sender means stronger magnetic field = higher reading on the needle. (The amp-meter works on magnetic field)
But on these gauges there is a bimetal strap. Bimetal is two different metals fused together, forming a seemingly solid piece of sheet metal. The two metals are chosen because they expand differently when heated. The strap is then wrapped in a thin wire that has a little resistance built in to it. When a current is run through the wire it will heat up. It heats the bimetal that bends. More heat = more bending. This is what moves the needle.
So how did my repair work out? Well, it didn't. Ran with VDO gauges. But then I got an idea. Maybe I didn't have the correct resistivity in the wire i had wrapped on. Built a variable voltage regulator. A kit, just soldered together. 5 volts wasn't enough. Turned the voltage up a bit and behold, the gauges worked! Extremely important to get the correct wire. I later replaced them with professionally repaired gauges.