Hello Eric:

Of course, you can test any arbitrary linear combination of the coefficients
that you choose. But the question is whether a particular test is of any
interest.

It's usually a good idea to write down the mathematical formula that you are
using to model the data. Although you are using 3 time lags, I'll just use
a single time lag to simplify things. Then the model would look like:

z(t) = b0 + b1*t + cW(t) + dH(t) + eV(t) + err(t)

where
z(t) = fMRI data
b0 = constant coef.
b1 = linear drift coef.
W(t) = indicator function for warm stimulus
H(t) = indicator function for hot stimulus
V(t) = indicator function for very hot stimulus
err(t) = measurement error

The above indicator functions are 0 or 1, depending on whether the stimulus is
present or not at that time point. Statistical tests will usually involve
tests of the coefficients c, d, and e.

The first GLT that you listed, which for a single time lag would be:
0 0 -1 1 1
is actually a test of:
Ho: -c + d + e = 0, vs. Ha: -c + d + e <> 0,
or, equivalently:
Ho: c = d + e, vs. Ha: c <> d + e.
So, this GLT is a test of whether the response to the warm stimulus is equal
to the SUM of the responses to the hot stimulus and the very hot stimulus.
But this test is probably not of interest. For example, suppose that the
response to all stimuli is the same: c = d = e = 57 (say). Further, suppose
that the measurement error is negligible. Then, with the above GLT, you would
reject the null hypothesis, since 57 <> 57 + 57 = 114. Thus, in this case you
would have a positive result. It's just not clear what this result means.

The second GLT that you listed, which for a single time lag would be:
0 0 -2 1 1
is actually a test of:
Ho: 2c = d + e, vs. Ha: 2c <> d + e.
or, equivalently:
Ho: c = (d + e)/2, vs. Ha: c <> (d + e)/2.
This GLT has the interpretation that you are testing whether the (average)
response to painful stimulus is different from the response to warm stimulus.
This would seem to be more meaningful. Note that, for the previous example
with equal response to all stimuli, this GLT would NOT reject the null
hypothesis.

Other GLT's that might be of interest:
0 0 -1 1 0
Which is a test whether response to hot stimulus is different from the response
to warm stimulus.
0 0 0 -1 1
Which is a test whether response to very hot stimulus is different from the
response to hot stimulus.

In each case, you should probably restrict consideration to just the set of
voxels for which the Full Model is statistically significant (i.e., those
voxels which pass the Full Model F-stat threshold).

Doug Ward