Problem is fixed - a least, I get values for a few hours now...
Here's the patch to OneWire.cpp:
--- OneWire_orig.cpp 2008-05-20 02:10:54.000000000 +0200
+++ OneWire.cpp 2009-04-14 19:30:58.000000000 +0200
@@ -115,8 +115,8 @@
// more certain timing.
//
void OneWire::write_bit(uint8_t v) {
- static uint8_t lowTime[] = { 55, 5 };
- static uint8_t highTime[] = { 5, 55};
+ static uint8_t lowTime[] = { 60, 8 };
+ static uint8_t highTime[] = { 8, 60};
v = (v&1);
*modeReg |= bitmask; // make pin an output, do first since we
@@ -137,7 +137,7 @@
*modeReg |= bitmask; // make pin an output, do first since we expect to be at 1
*outputReg &= ~bitmask; // zero
- delayMicroseconds(1);
+ delayMicroseconds(3);
*modeReg &= ~bitmask; // let pin float, pull up will raise
delayMicroseconds(5); // A "read slot" is when 1mcs > t > 2mcs
r = ( *inputReg & bitmask) ? 1 : 0; // check the bit
As you can see, I had to adjust the timing a little bit. As far as I understand the specifications, I think the original timings in OnwWire.cpp are at the minimum allowed. I now put the values a little bit more to "safe" mode 
And I also had to replace the 4k7 resistor with a 2k2.
I'm not sure how to contact Tom - maybe he is reading this post