Do processes involving synthesis need heat?
Definitely. Although combination processes may be exothermic, they do have activational energy. As an example, consider the reaction:

$$\ce{H2 + I2 -&gt; 2HI}$$

While the formation of two $\ce{H-I}$ bonds is quite energy releasing, you still have to go through breaking a $\ce{H-H}$ and a $\ce{I-I}$ bond. You need to supply heat to give thermal agitation to allow the molecules with sufficient energy to break the bonds. A typical reaction like this one would have this energy-reaction coordinate graph:



The reaction proceeds into a high-energy transition state, and then comes down to the low energy products. To reach the transition state however, you must supply heat. 

Edit: As @porphyrin mentioned, there are some reactions that have essentially zero activational energy. Combination of radicals may be an example:

$$\ce{Cl. + Cl. -&gt; Cl2}$$

This one has no activational energy because there is no unstable transition state involved. Another popular example is the basic neutralization reaction:

$$\ce{H+ + OH- &lt;=&gt; H2O}$$

Here again, there isn't any highly unstable transition state.