Regulated power supply from thermostat to zigbee module
The MCP1703 requires 0.625V overhead to regulate a 3.3V supply when taking 250mA. This means it needs 3.925V for it to work correctly. However if you are only taking 25mA the drop-out voltage is more like 0.1V and this means you will be OK: -



There are more detailed graphs of other output voltages and their respective drop-out voltages but this one is closest to +3.3V

It'll work fine with the capacitors you specified - you just need to check what current your zigbee circuit might take under worst-case conditions. If in doubt make the regulator's output capacitance 10uF or larger but i don't think you'll need larger than 10uF