My Turion 64 ML-37 arrived so I gave it a quick test. I got it from local laptop spare parts shop, not as cheap as previous ML-34 but not crazy expensive either.
I received 20x20mm copper shims with 0.5mm thickness so I used one on CPU die, with thermal paste on both the die and upper side of the copper shim. Thermaltake MaxOrb EX (full copper) went on top and the mounting screw wasn't tightened all the way, about 1mm remained. Mounting pressure is very good and the issue with bad die contact is gone.

- we have up to 10x CPU multiplier in BIOS
- same as ML-34 at 2.2Ghz Async Latency value 6ns doesn't work so we have to use 7ns. It doesn't reboot but memtest fails within a minute.
- at 2.2Ghz the CPU seems to be running so cool CPUID HWMonitor is unable to take a good reading and reports 18'C. Aida64 shows 2 sensors and one of them reports remperature this low, another one reports more reasonable 25'C when idle. With Super PI 32M running the temperature is 30/29'C on each sensor. Prime95 manages to heat it up to 31/29'C. Not sure if it's a sensor defect or the CPU really runs this cool.
- same as ML-34 Command Rate 1T isn't stable with 2 memory sticks at 2403Mhz CPU, 267Mhz base, 9x multiplier, HT 801 (3x), 400 memory. Super PI 32M fails within a minute.
- at 2.6Ghz and conservative memory timings it does boot into Windows XP but it eventually bluescreens. Quick 5 minute memtest passes. Probably higher voltage than 1.4V is needed, maybe ML-40.
It is clear that getting Turion 64 to run at 2.4Ghz requires Command Rate 2T and more voltage for higher frequency. In my opinion not worth chasing, just get s939 (Toledo) or AM2 (Windsor).
My recommendation would be not to chase Turion 64 ML-37 or faster clocked variants, they are extremely rare, just get ML-34 which are cheap (€10) and run them at 2209Mhz CPU, 260Mhz base, 8.5x multiplier, HT 779 (3x), 400 memory (Command Rate 1T). The CPU is 4% faster than Clawhammer 3400+, consumes less power and has SSE3. My CPU cooler fan runs at 1200 RPM, but you can get a slower one at 800 RPM.
Pentium III 900E,ECS P6BXT-A+,384MB,GeForce FX 5600, Voodoo 2,Yamaha SM718
Turion 64 ML-37@2.2Ghz,Gigabyte GA-K8NE,2GB,GeForce GTX 275,Audigy 2ZS
Phenom II X4 955,Gigabyte GA-MA770-UD3,8GB,GeForce GTX 780
Vishera FX-8370,Asus 990FX,32GB,GeForce GTX 980 Ti