your thermostat is shut and open once it has reached the temp it was designed for, this will be usually be on the stamped on thermostat.
once it opens, the cooling system will become fully functional.
if it opens at a lower temp, it will take longer to heat up to the manufacturers intened temp.
so thats the technical bit, heres my first hand experience-
when i had heatings problem with my own car i changed to the trd stat and it delayed it overheating.
i had thermostat setups and each one caused the results i expected.
1.the first was the stat that was in the car from japan which the engine overheated with
2.the second was a new oem stat from toyota, which opened bit later than the stock one(tested in a bowl of boiling water) and resulted in the engine overheating quicker than the first stat i had.
3.the third was a trd stat, 72degrees c, which opened first of the three stats(bowl) and also made the engine take longer of the three to overheat
4.as i decided i wouldnt use the oem stat, i cut the middle out and just used it to keep the seal on the housing.this took the longest, by far, of the 4 for my engine to overheat
in terms of how i measured when the engine overheated, well i drive the same route to work and take roughly the same amount of time everyday, give or take a few minutes, so it was obvious to me which stat took the longer amount of time for the engine to overheat.
so yes, it does take longer to heat up, i experienced it first hand