Can police inspect my house with special, technological equipment without a warrant?
It depends. Courts have generally ruled that if the technological equipment is used by or available to the general public (such as a thermo-imaging scanner, which detects heat), then police will need a warrant inspect your house with it. Likewise, phone taps and other technologies that require an initial physical intrusion to set up (like a bug) will require a warrant. However, technologies available to the general public (such as a battery operated radio) used to hear or inspect the inside of a house do not require a warrant, even if used by a government official.
Moreover, aerial photography - which is commonly used and available - does not require a warrant, unless sophisticated surveillance equipment (such as satellite technology) is required.