Inverse thermoremanent magnetization (ITRM) is reversed to the thermoremanent magnetization (TRM) process: ITRM results from warming from low temperature T in a magnetic field, while TRM results from field cooling from high T. The development of ITRM was studied in magnetites of grain sizes from submicron to 135 ¿m, in pyrrhotites and in hematite crystals. All three minerals acquired ITRM after warming through their magnetic transitions (35 K for pyrrhotite, 120 and 130 K for magnetite, 250 K for hematite). However, when an impacting meteorite's cold interior warms to ambient T in the geomagnetic field, magnetite is the most likely candidate for acquiring ITRM. The magnetite ITRM blocking temperature distribution was determined from 12 neighboring partial ITRMs in nested field-on warming plus field-off cooling cycles (300--20 K). The largest partial ITRMs are produced in T intervals around magnetite's Verwey transition (TV = 110--120 K) and isotropic point (TK = 130 K). Both transitions involve large changes in crystalline anisotropy and renucleation of magnetic domains. ITRM is blocked when initially broad domain walls narrow and are pinned by dislocations. ITRM has contrasting properties to TRM, which is mainly due to blocked single-domain moments. ITRM is strongest for 3- to 20-¿m grains, whereas TRM peaks for submicron magnetites. Only 10--20% of ITRM survives low-temperature demagnetization (LTD) at 77 K or AF demagnetization to 10--15 mT, compared to 30--90% for TRM. ITRM decreases quasi-linearly with T in thermal demagnetization. The median unblocking temperature TUB is ≈300¿C and 20--25% survives at 550¿C. The low-TUB part of ITRM could mimic extraterrestrial NRM of low TUB, cited as evidence of negligible heating of meteorites in their transfer to Earth. The high-TUB ITRM would contaminate paleointensity determinations up to the highest T steps. The best cure for ITRM contamination is AF or LTD pretreatment.