Can I accelerate the cure time for acrylic caulk?
Well, DAP Dynaflex 230 is a great caulk, but like all other acrylic caulks that I used, they specifically state that curing time is longer in cool or humid conditions. 

See their TDB:


  
  Apply in temperatures above 40°F (4.44 °C).
  Do not apply if rain or freezing temperatures are forecasted before full cure can occur. Cold weather and high humidity will slow down cure time.
  


So yeah, if you're applying it in cold and wet weather, it will take longer to cure, so moderate heat might help (application temperature is up to 100F/38C, don't just bring a heat gun to it), as well as shielding it from elements.