Controlled trapping of cells and microorganisms using substrate acoustic waves (SAWs; conventionally termed surface acoustic waves) has proven useful in numerous biological and biomedical applications owing to the label- and contact-free nature of acoustic confinement. However, excessive heating due to vibration damping and other system losses potentially compromises the biocompatibility of the SAW technique. Herein, we investigate the thermal biocompatibility of polydimethylsiloxane (PDMS)-based SAW and glass-based SAW [that supports a bulk acoustic wave (BAW) in the fluid domain] devices operating at different frequencies and applied voltages. First, we use infrared thermography to produce heat maps of regions of interest (ROI) within the aperture of the SAW transducers for PDMS- and glass-based devices. Motile Chlamydomonas reinhardtii algae cells are then used to test the trapping performance and biocompatibility of these devices. At low input power, the PDMS-based SAW system cannot generate a large enough acoustic trapping force to hold swimming C. reinhardtii cells. At high input power, the temperature of this device rises rapidly, damaging (and possibly killing) the cells. The glass-based SAW/BAW hybrid system, on the other hand, can not only trap swimming C. reinhardtii at low input power, but also exhibits better thermal biocompatibility than the PDMS-based SAW system at high input power. Thus, a glass-based SAW/BAW device creates strong acoustic trapping forces in a biocompatible environment, providing a new solution to safely trap active microswimmers for research involving motile cells and microorganisms.