Cold loop checking is done without powering up, ie the wiring integrity is tested through loop resistance and continuity check. Where as the hot loop checking is done by simulation of the automation controller (PLC, DCS) and the I/O, Functions etc. are tested.
Cold Loop checking: Checking of wires continuity of respective field instrument-Junction box-DCS/PLC marshaling panel terminal.
Hot loop checking: Once you power up your field instrument through DCS/PLC system, by stimulating process input from respective field instrument and cross check its response at DCS/PLC system