There's a lot of good general advice in this thread, but for the above statement, respectfully, I disagree.
If you've just kicked a football and strained (say) your rectus femoris, the single best thing you can do is ice it. Cooling the tissue has a number of benefits:
- stimulation via the autonomic nervous system to reduce blood flow (you have already stated this, I know - but it is very important in the acute state post-injury namely
1) minimising swelling, therefore minimising muscle inhibition and subsequent atrophy
2) minimising inflammatory infiltration, reducing cellular damage caused by the inflammatory cascade AND release of pain causing chemicals such as substance P
- physically reducing the cellular metabolic activity
- physically reducing pain fibre conduction velocity (i.e. less pain transmission)
Of course, in the sub-acute phase, reducing these processes are less important - so heat therapy is more effective.