Why is temperature regulation an important factor for producing explosives?
My advice on TATP is simple: 

If you're an inexperienced amateur researcher, do the synthesis on paper - and only there! 

Actually, the synthesis on TATP can be performed at temperatures above 0 °C. When Richard Wolffenstein accidently found in 1895 during his works on coniine that TATP had been formed in a mixture of 10% hydrogen peroxide and acetone, he did not use any acidic catalyst and had kept the mixture at room temperature for weeks:


  Ueber die Einwirkung von Wasserstoffsuperoxyd auf Aceton und Mesityloxyd, Ber. dtsch. chem. Ges., 1895, 28, 2265-2269 (DOI)


When he had collected the precipitate and recrystallized it from diethyl ether, it exploded, which Wolffenstein attributed to to the formation of peroxides in ether.

One of the first reports on the synthesis of TATP under acidic conditions was given by Milas and Golubovic:


  Studies in Organic Peroxides. XXVI. Organic Peroxides Derived from Acetone and Hydrogen Peroxide, 
  J. Am. Chem. Soc., 1959, 81, 6461-6462 (DOI)


Btw, the experimental part of this article starts with


  These peroxides are dangerously explosive and should be handled with extreme care.


Under controlled lab conditions, the decomposition of TATP in solution seemingly has been examined:


  J.C. Oxley, J.L. Smith and H. Chen, 
  Decomposition of a Multi-Peroxidic Compound: Triacetone Triperoxide (TATP), Propellants, Explosives, Pyrotechnics, 2002, 27, 209-216


and the activation energy for this first-order reaction was calculated to be around $\mathrm{150\,kJ\cdot mol^{-1}}$.

What makes TATP different from most of the other known explosives is 


the molecule (obviously) does not contain nitro groups. Typical detectors for explosives thus fail here. Together with the simplicity of the synthesis, this is a real problem in law enforcement!
the explosion does not generate a lot of heat, but is an entropic explosion.


The latter was througly examined by Ehud Keinan and coworkers:


  Decomposition of Triacetone Triperoxide Is an Entropic Explosion, J. Am. Chem. Soc., 2005, 127, 1146-1159. (DOI)


If you don't want to go though all their calculations of a possible decomposition mechanism, the following hopefully is impressive enough:


  The approximate pressure increase, assuming an
  infinitely rapid conversion that occurs in the volume of 1 mol
  of solid 1 (=TATP), is of the order of 100 bar. The associated energy
  content is approximately 2500 kcal/mol. This is the origin of
  the explosive power of solid 1.


I'm aware that I probably haven't fully anwered your question, but as a take-home message I can only suggest again to not attempt any experiment with this peroxide!