Following up from my earlier posting. The technician at Toyota took an hour this morning, spraying and digging mud out of the engine compartment before he could diagnose the problem. In brief, a mangled radiator. Not leaking, just a bit . . . um . . . resculpted. They're ordering in the new rad for me, so I need to go back to the dealership tomorrow morning to have it installed. Could have been much worse, I suppose.
Update: In the cold light of day, the damage didn't look too bad (from the outside, anyway):
Visitors since 17 August, 2004