According to various aspects, exemplary embodiments are disclosed of solar thermal collectors, solar heating systems, and thin plate heat exchangers and absorbers. The thin plate heat exchangers and absorbers may be used for solar applications and/or non-solar applications. In an exemplary embodiment, a solar thermal collector generally includes a first layer comprising polymer and configured to allow sunlight to pass therethough. A second layer comprises polymer and is configured to absorb thermal energy from sunlight. The second layer includes edges heat sealed to edges of the first layer. A permeable core is disposed between the first and second layers. In operation, a heat transfer fluid may flow through the permeable core and directly contact the second layer, whereby thermal energy is transferrable from the permeable core and the second layer to the heat transfer fluid.