user58194: So I want to make an Arduino based thermostat controller. I'm good with the semantics behind this, there's just one detail I want to make sure I get right: Power
I know US thermostat power is 24VAC, but I'm not sure how to convert that to 12V 0.5A DC that the Arduino wants. I'd like to do this efficiently rather than generating a ton of heat in the process, too. I don't even know how many amps "24VAC" is, which is the only specification I can find on thermostat power.
I've found 24VAC to 12VDC converters (made for surveillance cameras) online, but most are rated for 1.5A, and I'd be concerned about frying the Arduino. I am not sure if the Arduino only pulls as much as it needs, or if it would try to pull the full 1.5A and destroy itself. I also do not know if these are relatively power efficient, either.
I'm generally hoping someone has been down this path before so that I don't have to reinvent the wheel.

user30175: 
I don't even know how many amps "24VAC" is

Exactly, because that's a voltage rating (24 Volts AC) and no information about the current capability is given.

I've found 24VAC to 12VDC converters (made for surveillance cameras) online, but most are rated for 1.5A, and I'd be concerned about frying the Arduino. I am not sure if the Arduino only pulls as much as it needs, or if it would try to pull the full 1.5A and destroy itself

The Arduino, as a semiconductor, will consume only the current it needs. What current it needs is determined by the processor core (if it's e.g. in sleep-mode or not), the activated peripherals (ADC etc) and devices powered externally via the Arduino's +5V or +3.3V pins. 
The typical power consumption of an Arduino board running a sketch (no low-power mode + no external devices) is about 20mA, aka 0.020A.  
Also note that what's happening is when you feed +12VDC into the VIN pin, it goes to a linear voltage regulator, which converts excess voltage into heat while keeping the current the same. The official Arduino Uno (not a chinese clone!) has a NCP1117ST50T3G, which is a 6.5V-20V (recommended limit:12V) to 5V linear regulator with I_out of minimum 1A, typical 1.5A (also note I_out is circa I_in, the regulator itself needs negligable current). Clones might use a cheaper (and worse) voltage regulator. Also note that this output capability might not be realisitically achievable without a heat-sink on the regulator; since excess voltage is converted into heat, converting +12V to +5V at 1A creates (12V-5V)*1A = 7W of heat(power). The package cannot sustain that for very long and the regulator shuts down due its built-in thermal protection.  
In short it can be said that it's not a problem to connect a higher-rated power supply to an Arduino. The Arduino will pull what it needs to power itself and everything else on the +5V and +3.3V pins, if it's within the limits of the voltage regulator. 
These videos might help your understanding of linear voltage regulators: https://www.youtube.com/watch?v=GSzVs7_aW-Y https://www.youtube.com/watch?v=giGRrODKJSE

58194: <p>So I want to make an Arduino based thermostat controller. I'm good with the semantics behind this, there's just one detail I want to make sure I get right: Power</p>

<p>I know US thermostat power is 24VAC, but I'm not sure how to convert that to 12V 0.5A DC that the Arduino wants. I'd like to do this efficiently rather than generating a ton of heat in the process, too. I don't even know how many amps "24VAC" is, which is the only specification I can find on thermostat power.</p>

<p>I've found 24VAC to 12VDC converters (made for surveillance cameras) online, but most are rated for 1.5A, and I'd be concerned about frying the Arduino. I am not sure if the Arduino only pulls as much as it needs, or if it would try to pull the full 1.5A and destroy itself. I also do not know if these are relatively power efficient, either.</p>

<p>I'm generally hoping someone has been down this path before so that I don't have to reinvent the wheel.</p>
 30175: <blockquote>
  <p>I don't even know how many amps "24VAC" is</p>
</blockquote>

<p>Exactly, because that's a voltage rating (24 Volts AC) and no information about the current capability is given.</p>

<blockquote>
  <p>I've found 24VAC to 12VDC converters (made for surveillance cameras) online, but most are rated for 1.5A, and I'd be concerned about frying the Arduino. I am not sure if the Arduino only pulls as much as it needs, or if it would try to pull the full 1.5A and destroy itself</p>
</blockquote>

<p>The Arduino, as a semiconductor, will consume only the current it needs. What current it needs is determined by the processor core (if it's e.g. in sleep-mode or not), the activated peripherals (ADC etc) and devices powered externally via the Arduino's +5V or +3.3V pins. </p>

<p>The <a href="http://www.home-automation-community.com/arduino-low-power-how-to-run-atmega328p-for-a-year-on-coin-cell-battery/" rel="nofollow noreferrer">typical power consumption</a> of an Arduino board running a sketch (no low-power mode + no external devices) is about 20mA, aka 0.020A.  </p>

<p>Also note that what's happening is when you feed +12VDC into the VIN pin, it goes to a linear voltage regulator, which converts excess voltage into heat while keeping the current the same. The <a href="https://content.arduino.cc/assets/UNO-TH_Rev3e_sch.pdf" rel="nofollow noreferrer">official Arduino Uno</a> (not a chinese clone!) has a <a href="https://www.onsemi.com/pub/Collateral/NCP1117-D.PDF" rel="nofollow noreferrer">NCP1117ST50T3G</a>, which is a 6.5V-20V (recommended limit:12V) to 5V linear regulator with I_out of minimum 1A, typical 1.5A (also note I_out is circa I_in, the regulator itself needs negligable current). Clones might use a cheaper (and worse) voltage regulator. Also note that this output capability might not be realisitically achievable without a heat-sink on the regulator; since excess voltage is converted into heat, converting +12V to +5V at 1A creates (12V-5V)*1A = 7W of heat(power). The package cannot sustain that for very long and the regulator shuts down due its built-in thermal protection.  </p>

<p>In short it can be said that it's not a problem to connect a higher-rated power supply to an Arduino. The Arduino will pull what it needs to power itself and everything else on the +5V and +3.3V pins, if it's within the limits of the voltage regulator. </p>

<p>These videos might help your understanding of linear voltage regulators: <a href="https://www.youtube.com/watch?v=GSzVs7_aW-Y" rel="nofollow noreferrer">https://www.youtube.com/watch?v=GSzVs7_aW-Y</a> <a href="https://www.youtube.com/watch?v=giGRrODKJSE" rel="nofollow noreferrer">https://www.youtube.com/watch?v=giGRrODKJSE</a></p>
