As Barry talks to Snart at the prison, his jacket is on the chair. When he stands up and walks to Joe, he leaves the jacket on the chair. When both leave, suddenly Barry has his jacket in his hands.
Thermite isn't explosive. It's an incendiary (it burns very hot). "Thermite residue" would be everywhere since a primary component is rust.
While it's true that infrared can be used to detect heat, ultraviolet cannot be used to detect cold. Though bluish colors are popularly associated with cold, blue light is in fact hotter than red light, and ultraviolet radiation is far hotter than infrared, hence the danger of sunburns. A very cold body would emit radio waves.
A laser alarm system doesn't sound the alarm, but prevents it from being sounded. Thus any interruption, such as somehow freezing the light, sounds the alarm.