An DC10 flight crew reported a flap disagree anomaly that ultimately resulted in a full slat no flap landing.

Narrative

While returning to blocks to address a cooling fan problem; we accomplished the After Landing Checklist and could not get the flaps to retract. Checked out by Maintenance and signed off as 'Flaps ops checks good at this time'. We then started all 3 engines and performed a check of flaps at all detents. No further problems presented so we took off. The First Officer called for 'Flaps Up' on schedule and; soon after; we got a 'FLAP DISAGREE' warning. Rapidly accelerating toward 250 KIAS and with no flap asymmetry or adverse flight tendencies; I prompted and the First Officer called for 'Slats Retract'; hoping the flaps and slats would normalize and retract. Flaps stopped around 7 degrees; so I went to QRH Checklist which directs a return to the original flap/slat position; which we complied with and the flaps and slats indeed moved to takeoff position of 12.8. While [we were] coordinating with ATC for a block of 6-10;000 FT and vectors to remain in airport vicinity; the flaps and slats slowly moved to zero/retracted uncommanded.We then contacted the Duty Officer and he wanted us to configure and plan for a normal landing; however; faced with uncertain flap and slat positions on final; we made initial plans for a No Flap/No Slat approach and landing. The First Officer and I independently determined that a No Flap/No Slat landing would require less than 8;200 FT after correction for non-standard day from charts; but Vapp would be 206 KTS and Vref would be 201 KTS; above the 195 KTS tire limit. An approach at the same weight; normal configuration would be 60 KIAS slower; but if flaps and slats were to again retract uncommanded; the results could have been catastrophic.We burned down to about 18;000 LBS total fuel over the next hour and continued to consult with the Duty Officer. He again urged us not to land in a 0/RET configuration. We looked at landing data and procedures for a 0/EXT landing. This would allow Vapp and Vref to be 172 and 167; respectively. As this was only 34 KTS short of No Flap/No Slat speeds; we felt we could accelerate quickly enough to go around if slats began retracting (given their relatively slow rate of retraction earlier) and come back around for a No Flap/No Slat approach if necessary.This became our final plan and was acceptable to the Duty Officer. We touched down uneventfully at 164 KIAS. We did experience a minor Brake Overheat on number 5 brake (581 degrees) when we got to our ramp. QRH was consulted again and; at our request CFR was summoned as a precaution. Maintenance inspected the brakes; we shut down engines and got towed into the gate. The only other human factor to consider in this matter is crew duty circumstances. Takeoff on this flight occurred 11 plus 37 into the Captain's duty day; 9 plus 22 into the First Officer's duty day; on the second flight of our duty day; after three pre-flights; two of them in extreme heat (37-38C).