detecting presence inside - PIR or ultrasound? (I am professionally a software guy working in the GCC compiler with MELT, so I am fluent in software, but much less in hardware - I did use a solder for a 74LS00 nand gate based stuff in the 1990s. This is my first Arduino project)

My first Arduino project would be to automate the lights and the fan in my inhouse WC toilet in Paris (France) suburb. I bought several Arduino Nano v3 boards. I'm thinking of driving with a relay a low voltage 12v LED lightbubble. I want to detect human presence in the toilets. I'm thinking of some PIR sensor, but I am afraid that PIR won't detect anything if the temperature is above 37°C (or about 100F), which is unusual in Paris (France) but may happen a few days per year (I've got no air conditioning). Is my worry correct, or can a PIR still work with very warm outside temperature? Should I use an ultrasound detector instead?
PIR sensors work fine and are probably easier to program for than ultrasonic sensors. For example, this tutorial on a PIR sensor sold by Adafruit has a datasheet at the bottom that says:

Operating Conditions Operating Temperature -20 ˚C to +70 ˚C
Storage Temperature -30 ˚C to +80 ˚C
Operating Voltage 3 to 10 V at Rs = 47 kΩ

You can try to find and check the datasheet for the sensor you intend to purchase to determine if it will work.