What is the best time to insert an ici insemination if you are using thawed semen?

1 day after LH surge. Many studies recommend inseminating one day after the lh surge. Some studies find an increased benefit with a second insemination to two days after the lh surge. In general with frozen thawed sperm, iui works better then ici.
Timing. 'best' depends 'how' you are timing the insemination. If using a home lh kit do the ici the day the test is positive. This will be more reliable than counting calendar days, and for most will be better than using bbt. Monitoring with ultrasound is more reliable still, but obviously requires us. A single insemination without a clear timing strategy is unlikely to be succesful.