It's not literal even in Itanium's case, as it's about leveling the voltage droop and not temperature.
There can be many other kinds of run-ups to steady state happening in processors for microbenchmarks. Caches/TLBs, branch predictors, clock gating, macro scale voltage/frequency scaling, memory prefetching, power management in the system outside cpu, etc.
How literal is the 'warm up' for the vector units? I've occasionally seen this effect mentioned with regard to microbenchmarking, but never understood why this might be. Are vector units actually slowly activated over several cycles so as to reduce voltage droop?