Microtubules (MTs) are cylindrical cytoskeleton polymers composed of α-β tubulin heterodimers whose dynamic properties are essential to fulfill their numerous cellular functions. In response to spatial confinement, dynamic MTs, even in the absence of protein partners, were shown to self-organize into higher order structures (spindle or striped structures) which lead to interesting dynamical properties (MT oscillations). In this study, we considered the assembly and sensitivity of dynamic MTs when in bundles. To perform this study, spermine, a natural tetravalent polyamine present at high concentrations in all eukaryote cells, was used to trigger MT bundling while preserving MT dynamics. Interestingly, we first show that, near physiological ionic strengths, spermine promotes the bundling of MTs whereas it does not lead to aggregation of free tubulin, which would have been detrimental to MT polymerization. Experimental and theoretical results also indicate that, to obtain a high rate of bundle assembly, bundling should take place at the beginning of assembly when rapid rotational movements of short and newly nucleated MTs are still possible. On the other hand, the bundling process is significantly slowed down for long MTs. Finally, we found that short MT bundles exhibit a higher sensitivity to cold exposure than do isolated MTs. To account for this phenomenon, we suggest that a collective behavior takes place within MT bundles because an MT entering into a phase of shortening could increase the probability of the other MTs in the same bundle to enter into shortening phase due to their close proximity. We then elaborate on some putative applications of our findings to in vivo conditions including neurons.