Motion sensors are NOT pet-friendly

Did you mount the sensors ~4-5 off the ground and upside down?  

Some very good information in this USER CREATED document on SS3 operations: https://simplisafe.com/forum/customer-support-forum/installing-and-using-simplisafe/ss3-first-pass-at-a-manual

I'm having the exact same problem. I had 2 false alarms tonight because one of our motion sensors is picking up my 16lb dog. I feel really misled by this company, their website says they don't pick up small dogs, I even turned the sensitivity down to low but I will not turn the motion upside down. First, this wouldn't work because my dog jumps on the furniture and second, their solution basically advertises the blindspot and tells thieves how to beat the system! You can rob a simplisafe customer with pets because there's a 4-ft blind spot in every room with motion sensor.

I have my motion sensor about 5 feet off the ground, button-side up - our 12lb cat triggers a notification nearly every day. She doesn't even need to climb onto the couch cushions in order to trigger a notification, the sensor seems to detect movement when she's slowly strolling along the ground (when referencing the camera). The reality is that the sensor is NOT designed to "distinguish the heat signatures of humans from those of pets", as the advertising brief claims.

I'm happy with the system otherwise, but this is a disappointing failure and it requires me to pick up entry sensors for every door and window on the main floor.

You could try removing the sensor from the wall and moving the sensitivity switch on the back of the sensor to "Low" and see if that helps.

As near as I can tell, the motion sensors are actually aimed, directional, heat change sensors, and that seems to be the situation with ALL motion sensors.

For a motion sensor to work in a pet household, you need to find a location that will be triggered at human walking height, but not at pet height (including jumping on furniture. It is possible that a pet's favorite room should not be protected with a motion sensor.   I suspect you will have this problem with any motion sensor on the market.  With all motion sensors, placement is everything.

(BTW, turning the sensor upside down, aims the diagonal direction upwards, while the regular way aims the direction downwards).

I have 11 cats, 3 motion sensors, and no problems. Mount it high, test button up, and make sure there is nothing horizontal in the field of view like a couch that cats can run across. By all means adjust the 3-position slide switch on the back of the motion sensor to something other than HI sensitivity. Also good if you can make it so the cats only walk toward the sensor rather than side-to-side. For example, better if located at the end of a hall instead of in the middle of the hall.

Gradual room temperature changes also should not be a problem, since it averages out the reading. But if it views at a ceiling vent, well yes it will trigger when the heat blows. Also the sudden appearance of sunlight on a wall will cause an alarm. Finally, the sensor is battery operated and restricted by the FCC to not send out signals too often. For this reason you have to wait a couple of minutes after triggering to expect it to sense you again. Otherwise you can parade an elephant in front of it and it won't see it.