Hollow thermoexpandable particles or microspheres are provided that contain hydrocarbon blowing agents and have a shell polymer that can be softened at the onset of the expansion temperature and solidified at a higher temperature (thermoset) in an expanded state. Preferably, the microspheres have a shell of thermally expandable and thermally crosslinkable polymer and a hollow interior that contains a hydrocarbon liquid that boils at a temperature below the heat activated crosslinking temperature of the polymer shell. The crosslinking of the shell polymer during or after expansion, which is heat activated at an elevated temperature, can solidify the shell polymer and, then, maintain the expanded volume of the microspheres. The thermoexpandable thermoset polymer particles are useful in insulation, packaging, for making foam materials such as polyurethane or polyisocyanurate rigid foams. The invented thermoset microspheres can substantially improve the close cell percentage and compressive strength of the foam materials and make the foam manufacturing less hazardous.