Most analog gear has SOME type of temperature control. Tempco resistors (low resistance change with temperature), thermisters (couple a positive response to a negative response to cancel out) or other techniques (e.g. heaters - get the circuit up to max temp asap and keep it there).

But none of that prevents temperature differences, they just control for them. And you wouldn’t use temp control everywhere - just where it’d effect the sound dramatically i.e. keeping your main voice oscillators in tune, not keeping your cowbell at a precise frequency

This is correct. I have a couple of analog oscillators in my modular rack and the case needs to heat up for a couple of minutes before they generate a stable pitch. Not familiar with the exact reasons to be honest.

The temperature sensitive part in a VCO is actually the exponential converter inside, which has a strong temperature dependence. This is because the current through a transistor depends on the ratio V_BE / V_T, and V_T is proportional to temperature.

It's a neat trick that lets you build good temperature sensors out of transistors, which is very convenient, but in these VCOs you have to add temperature compensation to the exponential converter, and the temperature compensation is far from perfect.

If you take linear VCOs (instead of 1V/octave exponential), they'll be much more temperature stable.

Higher quality equipment that needs a stable timebase will use ovenized oscillators with an integrated heater and a control loop to maintain a stable temperature. These are all inaccurate before they are up to operating temperature.

TVs and CRT monitors were common to change the shape and color of the picture as it got to temp. You never made critical color decisions on a monitor that hadn't been on for at least 15 minutes, preferably 30.

Basically all components have temperature dependent values