The most obvious, and perhaps the most satisfying way to do this is to give the planet two suns - one that provides light and one that provides heat. The problem is, how do you get one sun to appear only when the other does not?
Some other answers have suggested that the planet could orbit close to a brown dwarf (or hot gas giant, which is essentially the same thing), while the brown dwarf itself orbits a much more distant blue giant star. The brown dwarf would loom large in the sky as a dull red disk, warming the planet like a giant electric heater but not providing much light, whereas the blue giant, being so far away, would appear as a small but very very bright point of bluish white light, providing not much in the way of heat. (It actually gives out a lot more heat than the brown dwarf, but not so much of that reaches the planet since it's so far away. A substantial amount of light does reach the planet because blue giants are really, really hot and therefore give out an insane amount of light in comparison to the huge amount of heat they also give out.)
The problem is that as the planet orbits the brown dwarf the location of the two stars in the sky will change. Sometimes the planet will be between its two stars, so that one rises as the other sets, and then the days will be cold and the nights warm. But after the planet has progressed halfway around its orbit of the brown dwarf, the two stars will be near each other in the sky, and they'll rise and set at more or less the same time, just like on Tattooine. (Except that one star appears much bigger than the other in the sky.) Sometimes the 'day' star might even get eclipsed by the 'night' one. Depending on the orbital period of the planet around its brown dwarf, these seasons might cycle every week or so, or it might be a few years.
It's worth noting also that as well as giving out its own dull red light, the brown dwarf will reflect light from the blue giant, so it will have phases like Earth's moon, being 'full' when the stars are on opposite sides of the sky, and waning to a crescent and then a 'new sun' as they approach the same side. The unlit part will appear red and the lit part might be white, or it might be coloured, depending on what chemical processes are occurring in the upper layers of its atmosphere. (See the gas giants in our Solar system for examples of what this colouring might be like.)
This is all quite interesting, but what if you want the nights to always be hotter than the days, and not just sometimes? I can think of a couple of ways that might work, depending on what you want.
One way is to make the seasons change really slowly. If you make the "night" sun a red giant rather than a brown dwarf then you can put the planet really far away from it, because red giants are really really big and put out a huge amount of heat. Being far away means a slow orbital period. If the Sun became a red giant then the planets in the outer Solar system would receive enough heat to have liquid water, so you could make the orbital period a few hundred years. By giving the star a larger mass you could make it longer still. In this situation, the nights will be hotter than the days, but it would have been the other way around a few hundred years ago, and people might have legends about that.
The other way is to put your planet at what's called the "L1 Lagrange point" between the two stars. That's the point where their gravity exactly cancels out, so the planet can sit between them (but closer to the smaller one) without orbiting at all. This sounds ideal, except that the L1 point is a so-called "unstable equilibrium." Staying in that point is a bit like balancing on the top of a really tall poll - it doesn't take a lot of energy, but unless you keep shifting your weight in just the right way you'll fall down and end up somewhere else. This means your planet won't stay in that position by itself, but depending on what propulsion technology your world has, it might be possible to keep it there technologically. If you're looking for a high-tech solution, this might be it.