Afaik the transmission energy of a cell phone is limited to a maximum of 1 or 2 Watts (depending on which frequency it operates on). This power is a maximum that will only be used if the reception is bad.
In the wavie scene (people who are paranoid about radio waves controlling them) shielding those devices is a typical approach — this is also where the meme of the tinfoil hat comes from. Ironically that shielding makes your cellphone operate with the maximum transmission power at all times.
Even from transmitting heat to the phone's components itself or other items that are nearby, e.g. laptops: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5219578/.