Getting them outside and separate will help with airflow and reduce the temps.
All hay will rise in temperature for a while, but extremely wet hay has more of a chemical reaction that produces gasses that can combust as low as 160 degrees. Hay that has less than 15% moisture has little chance of combusting. Above that, you should watch it and at 20% moisture, you can start to have a real problem. You can drive a steel pipe into the rolls or bales and let it sit for there for about 15-20 minutes. If it is too hot to hold after that, you need to get the hay outside and monitor it. I believe they also make a probe thermometer that can be used.
The guy that rolls mine has a baler that constantly monitors the moisture content of the hay. Hayledge does not have this problem because the plastic keeps out the oxygen.
Edit: I found this link
https://www.farmanddairy.com/top-stories/how-to-prevent-hay-fires/415615.html
Critical temperatures:
125 F — No action needed
150 F — Hay is entering the danger zone. Check temperature twice daily and disassemble stacked hay bales to promote air circulation to cool the hay.
160 F — Hay has reached danger zone. Check temperature every couple hours and disassemble stacked hay.
175 F — Hot spots or fire pockets are likely. Alert fire services; stop all air movement around hay.
190 F — With fire service assistance, remove hot hay. Be aware that hay could burst into flames.
200 F or higher — With fire service assistance, remove hot hay. Most likely a fire will occur; Be aware that hay could burst into flames.