I am looking for a means, by RAW or RAI, to generate heat that can be used to provide lift for a balloon, or to power mechanisms that could generate lift, while not consuming fuel. While this most likely points to a spell or a magic item, I don't know which ones will allow me to make a hot air balloon (or something close to it).
Possibly the magic item Candle of the deep, a "common" magic item from Xanathar's Guide. This says it "gives off light and heat like a normal candle" — and it is unclear if it is consumed like a normal candle. Given that its major property (it burns underwater) is pretty boring in a world with the Light cantrip and the Continual Flame spell (the result of which is effectively a permanent torch which "cannot be smothered or quenched" so also presumably works underwater), it seems pretty reasonable that this magic item is not consumed. However, this would definitely be up to your DM — it's also reasonable to say "nah, it's just like a regular candle but works underwater".
Of course, even if they're not consumed, you'd need quite a few to provide lift for a balloon, but it is "common" ... so, getting a lot of them may be in the realm of possibility.
Create Bonfire might work
Create Bonfire creates a self-sustaining magic fire that lasts for 1 minute. However, as it is a cantrip, you can repeatedly re-cast it to keep the fire going longer. It can deal fire damage and ignite flammable materials in its area, so it definitely produces heat. However, it continues to burn even if no flammable materials are placed in its area. The spell has no material components. As long as you don't intentionally place any flammable materials (or flammable creatures) in the bonfire's space, this spell seems to satisfy all your requirements.
Create Bonfire might not work for a moving vehicle
Since you have added your reason for needing this spell, Create Bonfire may not be what you want. The bonfire created by the spell is stationary, but "stationary" is not clearly defined, leading to a number of questions about how certain spells work on moving vehicles, such as this one and this one. You should ask your DM how they will apply the rules in this case (or if you are the DM, you'll need to make a ruling).
Conjure Elemental might work. Given a 10-foot bonfire as raw material, it is able to summon a CR5 Fire Elemental for an hour, during which time it might be able to heat the air in your hot air balloon.
Additionally, the Eberron campaign setting uses bound elementals as the sources of motive power for their airships, so this sort of thing has precedent in official DND settings.
For generating heat, conjure elemental and create bonfire are pretty good spell choices. I'd also say anything that causes fire damage could also create heat, so anything with a long duration should work.
For magic items that already exist, I'd say Flame Tongue might be the go to if your DM agrees that fire damage is capable of heat. It stays burning as long as you hold it, so you could insert it into the burner of a steam engine. Or even do something cool like have the tip in the burner and the handle controls a rudder or whatnot.
Other industrial magical items
- Decanter of Endless Water: Not as good as the old days, since it requires constant operation, but infinite water. Use the weight or pressure to do things, move water wheels, fill stuff, etc.
- Eversmoking Bottle: Huge volume of smoke. No need to keep activating it. Fill a hot air balloon, or power an air pressure based system. It keeps releasing smoke to fill a large area. Depending on if you can get the gm to agree this creates pressure or not, you can do many things. There's also a discussion on whether the smoke is lighter than air or has any warmth to it.
- Ring of Telekinesis: Hard to get item, but any random person can now turn wheels or gears with 1000lbs of force without any effort. Pretty decent motor, just takes someone to operate it. Make sure to clamp the ring down so your operator doesn't steal it.