What are hot pickups
 

What exactly do hot pickups do? I am guessing you can't just turn up your volume...

Sorry let me restate... I think I understand that they can overdrive the preamp a bit. What about for full solid state? What does a hot pickup do in that case?

Solid state overdrives too. The amount of overdrive, and the tone of the overdrive, depends on the specific preamp design. "Hot" pickups just have a stronger than average output, for a variety of possible reasons. As far as overdriving any kind of preamp, all "hot" means is they overdrive the preamp sooner than average.

Hot pickups tend to have a boosted midrange and a lack of clear highs due to the larger amount of wire.

So when people say I am looking for hot pickups, are they looking for boosted mids? Might they get better results asking for pickups with boosted mids?

A "hot" pickup has more windings on the pickup coils than standard. This makes the pickup "louder" with a stronger signal, but there's a trade-off involved. As more and more windings are added, the pickup's self-inductance begins to reduce the treble relative to the mids and bass.

A little bit history ...

Until the 1970s dead pickups were mostly replaced with the pickups the manufacturer had at that time. If your 1959 P-PU died in 1971, it was normally replaced with a current 1971 P pickup.

During the 1970s some clever people had the idea that spare and replacement parts might be a good business - and this idea was gold.
These people not only copied the original pickups but tried to find benefits and different methods (like a hum canceling J pickup +++).

During the 1970s also japanese instruments with in the beginning poor pickups entered (or overflood) the market and (like nowadys) owners wanted to enhance their instruments with high quality pickups.

Now, normal replacement pickups (like the original) and "hot" pickups were offered. The mid/late 1970s were also the beginning of smooth high gain guitar overdrive. "Hot" pickups had a higher output and were also smoother than the original pickups.

The others already wrote about the typical "hot" sound.

"Wanted" bass distortion (through the whole gig) came much later than the 1970s.
Bass players like John TheOx Entwistle already played overdriven basses in the 1960s - but there is the question if he wanted to or simply had to (to be loud enough and compete with Pete Townshend).

Please keep in mind that there were always exeptions to the rule!
I don't want to say that 100% of all bass players fit to my "short history".

There's no way to increase your volume (to compete with Townshend) by using a hot pickup. If your amp delivers 200 watts the maximum of volume you'll achieve is 200 watts...

The difference between hot and not hot pups is tone (hotter=less bright and more mids). The hotness would depend on your amp power and pedals/preamps levels...

and output, ie voltage. Hot pickups put out more voltage than so-called "standard" ones as Bongomania pointed out.

The higher output drives the gain in the first stage of your amplifier, ie the preamp into distortion more readily.

And yes, the tone is inherently different, generally an increase in the mids. Partially because of the change in the resonant frequency and inductance from more windings.

2 ways to make a pickup hotter ... More windings which adds more ohms resistance or a stronger magnet will give a pickup more output.

Sometime hotter is defined as a mid boost. This will make the pickups distort more when any overdrive or distortion is used. Also the boost in mids can make the bass cut through the mix more.

"hot" pickups were great for rock guitar to get more crunch out of clean-ish tube amps back in the '70s. (think kiss or boston with dimarzio super distortion pickups pushing old non-master volume marshalls.)

these days guitar amps tend to have all kinds of overdrive gain, rendering super-hot pickups unnecessary or even counter-productive.

overly hot pickups for bass usually just end up being muddy, with reduced bass and treble.

Also hot can be induced by the material used. Ceramic pickups can have more output than regular pickups. My Dimarzio P model pickups are very hot. Hotter than my active Stingray pickup for example. The Dimarzio offer lots of everything: outplut, bass, highs and no muddy character. It does not quite sound like a Fender P pickup IMHO bu the tone is very nice nevertheless.

But... if you have a quiet bass, and your amp is already cranked, a hotter bass will be louder. It's just as if you turn down the volume control on your bass down to 5. Even if you have your amp on 10, that 200 watts is now not as loud as when the bass is on 10.

Hot pickups got started with guitar because louder pickups were able to over drive the lower gain amps at the time. Quieter pickups wouldn't, even with the amp on 10.

So in either case there is a perceived increase in loudness.

I prefer pickups that are not so hot, because they usually sound better.

Besides the possibility of magnetic interferance, does the pickup being closer have similar characteristics as hot pickup? Does a hot pickup further away where it would maybe send the same ?voltage? as a "normal" pickup still have the hot pickup sound?

The sensitivity of the pickup drops off with the square of the distance. So it's always better to have pickups closer to the strings if you want the most output.

Hotter pickups are never as clear sounding as lower output pickups. They have an exaggerated low end and the high end is rolled off. As you wind a pickup hotter, the resonant peak which occurs right before the high end starts to drop off, gets lower.

You can hear this in something like a Quarter Pounder. The leak is in the upper mids. This tends to make the pickup sound brighter, but it's harsher tone.

If you keep winding more wire you end up with something like a Gibson Mudbucker, where you have almost no high end, and lots of lower mids.

The opposite end of the spectrum are low impedance pickups, which are very clear sounding, with an extended high frequency response.

Yep, and this is true of G&L's MFD pickups too, for both basses and guitars. They have very high output, without the muted treble of heavily overwound traditional pickups. Some, however, find them harsh, especially with the instrument's volume up full. I don't find this with the split-coil in my SB-2, but of course strings and pickup height play their roles.

I guess if you crank your amp to 10 and you are using a hot pup you´ll get a clip/distorted signal... So if you want to retain clarity you could crank the amp with the weaker pup but not with the hotter... imo..

Yes, and the hotter pickup would be clear at lower volume levels either.