Which heats up faster, wood or glass?
2 Answers
It depends on the masses of the two substances and on the rates of heating.
Explanation:
If you have a much larger mass of one than of the other and heat both at the same rate, the one with the smaller mass will heat faster.
If you have the same mass of each but heat one at a much faster rate than the other, the one with the greater supply of heat will heat up faster.
But what if you heat equal masses of each at the same rate?
The specific heat capacity of a typical sample of wood is
The specific heat capacity of a typical sample of glass is
In other words, it takes twice as much heat to raise the temperature of 1 g of wood by 1 K as it does to raise the temperature of 1 g of glass.
If the heating rates are equal, the temperature of the glass will increase twice as fast as the temperature of the wood.
I know this is long. Bear with me! (You can skip the background information and still kind of get the idea.)
tldr; Wood is porous, storing heat inside crevices and insulating it in a confined space, preventing effective heat distribution. Glass is tightlypacked with semiconductive properties, transferring heat well throughout the glass. Therefore, the distribution of heat throughout glass is more effective and the average resultant temperature is higher.
BACKGROUND INFORMATION
If we take a statistical mechanics approach to this (I promise it won't be too crazy hard), I think it'll help. So, let's start with how we can determine the approximate heat capacity of a molecule.
According to the Equipartition theorem, we can approximate a compound's heat capacity through its degrees of freedom.
We often report this quantity in terms of
Depending on the structure of the molecule (monatomic, linear diatomic, linear polyatomic, nonlinear polyatomic), the distribution of which types of motions contribute most to the heat capacity of the molecule varies.
The degrees of freedom (DOFs) the following have are:

Monatomic  Translational (three DOFs);
EX: atoms

Linear diatomic  Translational (three DOFs), rotational (two DOFs), vibrational (one DOF, from
#3(2)  5 = 1# ; "symmetric" stretch);EX:
#"F"_2# 
Linear polyatomic  Translational (three DOFs), rotational (two DOFs), vibrational (depends on molecule);
EX:
#"CO"_2# has#3(3)  5 = 4# vibrational motions: symmetric and asymmetric stretch, and asymmetric and symmetric bend/wag (both degenerate, giving THREE unique ones). 
Nonlinear polyatomic  Translational (three DOFs), rotational (three DOFs), vibrational (depends on molecule);
EX:
#"CH"_4# , which has NINE vibrational modes from#3(5)  6 = 9# , but only FOUR unique ones (#A_1# ,#E# ,#2T_2# ).
The translational, rotational, and vibrational motions contribute to the heat capacity. Oftentimes, the electronic contributions are negligibly small.
MAIN POINT
The main point to take away from this is the idea of the vibrational contribution to the heat capacity. This contribution becomes more and more dominant as the size of the molecule increases, because then the number of different ways it can wag, stretch, and bend increases.
ACTUAL RESPONSE
Based on the composition of wood being about
Lignin:
Cellulose polymer:
The molecules can still only move linearly in three dimensions, and it can only rotate in three dimensions, but they have plenty of vibrational motions available. Lots of rotatable, nonrigid sigma bonds here that can stretch and bend.
Naturally, if a molecule can vibrate many different ways, it has many ways in which it can store/use heat energy through such motions.
Since wood is very porous, the heat gets trapped in these pores or crevices that are lined with these nonlinear polyatomics, and it's difficult for it to get out of the crevice and distribute throughout the wood, thereby slowing the heating process.
Unlike wood, glass is tightly packed (though amorphous), yet its composition of silica with boron dopant and other components can readily transfer heat throughout the glass due to their effective chargecarrier mobility as semiconductors, more quickly distributing the heat throughout the glass and increasing the average resultant temperature.
You can read more on the semiconduction mechanism here if you want background on semiconductors:
http://socratic.org/questions/canyouexplainthemechanismofdoping