How air temperature affects an ocarina's pitch
As described on the page 'The ocarina's breath curve', an ocarina's pitch is pressure sensitive. When an ocarina is made, the notes are tuned with a breath curve that produces a good sound. Ocarinas are usually tuned to concert pitch so they can play with other instruments. But there is a catch, as their pitch is also influenced by ambient air temperature. When you blow an ocarina, the voicing mixes your warm breath with ambient air from the environment, and the internal temperature stabilises between the two.
Ocarinas are tuned to play in concert pitch at a given temperature, such as 20°C. I call this the instrument's tuning temperature. If played with the same pressure, the pitch will be flatter in colder situations and sharper in warmer ones. As the ocarina's pitch is also affected by blowing pressure, you can compensate for this by raising or lowering your breath. This compensation is limited as the high notes are much less sensitive to pressure than the low.
If you have an ocarina, this can be observed easily. Just finger a low note and overblow it until the ocarina squeaks, tracking the starting note and the highest note with a chromatic tuner. If you repeat this same exercise on the highest note, you will not be able to push it anywhere near as far. Because of this irregularity, when playing in a colder environment, you have to increase your pressure more on the high notes than the low. Consequently, compensating for pitch means that the shape of the breath curve also changes.
The following graph visualises this effect: curve B represents the breath curve of a hypothetical ocarina at its original tuning temperature, the steeper curve C represents playing in a colder environment, and the shallower curve A playing in a warmer environment. Particularly, notice how a small change on the low end requires a larger change on the high notes. If your environment is considerably colder than the ocarina was tuned to play in, the high notes will squeak before you can push them into concert pitch.
Should you have also read the page on breath curves, you may have noticed that the graph is the same as the one that I used to demonstrate the breath curves of high and low pressure ocarinas. I am not being lazy; they are actually the same thing. Tuning an ocarina to play at a higher pressure requires blowing harder, and thus requires a steeper breath curve. Compensating for a cold environment also requires an increase in pressure and has the same effect.
How to deal with this as a player is covered on the pages 'Playing the ocarina in tune' and 'Dealing with warm and cold environments' but, in summary: to reliably play an ocarina in tune in different environments, you have to internalise how the breath curve changes in these situations. You also need an ocarina tuned to play at a temperature close to the environment you intend to play it in.
Pitch can be compensated for within a limited range and the pitch of an ocarina changes linearly at about 1 cent per degree Celsius (1.8°F), so a range of about plus or minus 15°C (27°F) from the tuning temperature is normally tolerable. This is limited by the high notes as they are so much less sensitive to pressure changes. Do note that playing towards the extremes of available compensation will not produce an ocarina's best sound.
Measuring best sounding pitch
If the tuning temperature is not known, best sounding pitch can be used as a basis. This is simply the pressure at which the high notes sound best in your opinion. To find your ocarina's best sounding pitch, play one of its high notes, such as the high E or F on a C ocarina. Notice that when you blow too softly, the note will sound weak and airy, while blowing too hard makes it airy and harsh. Pushing the note further will cause the ocarina to squeal. Vary your breath up and down to find a point where the note has the cleanest sound. The pitch can then be measured with a chromatic tuner.
Be aware that this may vary from what the maker intended. Because pressure affects timbre, a maker can intend that an ocarina be played at a given pressure for aesthetic reasons. Thus, you can't know an ocarina's tuning temperature unless you can get it from the maker directly. Also, an ocarina tuned to be loud will use more air and will sound more airy to the player. This airiness will be much less obvious to an observer at a distance.