Yes, it is typically possible to use a thermal imaging camera in this scenario. The reason is that such a camera is fundamentally sensitive to contrast in radiant flux, which depends not only on temperature, but also emissivity. Since emissivity varies between different substances, there can be sufficient contrast in apparent temperature to distinguish even between objects that are at the same actual temperature.
For example, given a piece of bare metal and a piece of glass at the same temperature, the radiant flux observed from the (low reflectivity, high emissivity) glass will principally be due to its own temperature, while that seen from the (high reflectivity, low emissivity) metal will predominantly be reflected from surrounding objects. Depending on what these objects are, the metal may be distinguishable from the immediate environment (e.g. if it is reflecting the sky, which has an effective temperature of roughly -50°C), or it may not be. Telling high-emissivity substances apart when they are close in temperature is often more difficult. By the same token, the actual temperature of high-emissivity substances is influenced more strongly by radiation from their surroundings than that of low-emissivity ones, because the former absorb more of the incident radiation.
Note that I chose glass as an example of a high-emissivity substance to highlight the difference between our ordinary experience and the situation in the long-wave infrared (LWIR). Glass has low emissivity in the visible region, but appears very different when observed in the thermal infrared--it appears "black" (strictly, as a black-body) rather than transparent. Substances such as silicon show somewhat opposite behavior, with high emissivity in the visible, but low in the LWIR.
To distinguish differences in real temperature from differences in emissivity, the approach is to measure the radiant flux at two or more different wavelengths. Then, the temperature is recovered from the ratio(s) of the measured flux(es) to one another, rather than their absolute values. However, this is rarely done in thermal imaging since it adds cost and complexity to what is already a costly and complex device. More typically a radiometric calibration is done, but this is not robust to changes in the scene being observed.
The characteristics of the detector also dictate what is or is not a resolvable difference in radiant flux.
HgCdTe (MCT) detectors operate as photodiodes, so they have good sensitivity (noise-equivalent temperature difference, NETD, down to about 10-20mK depending on operating temperature) and fast (sub-microsecond) response. If the read-out circuitry is saturated through observing a hot object, this can be addressed by reducing the integration time. However, these detectors must be cooled, otherwise internally thermally generated carriers dominate. If detection is done in an a.c. mode using a chopped signal, the operating temperature can be quite high (-30°C). If it is operated in a staring mode, cryogenic temperatures (77K/-196°C) are typically required. Temperature variations in the optics and chassis also affect the imagery, which can be a problem for outdoor operation. In addition to the cooling requirement, HgCdTe focal plane arrays (FPAs) are very difficult to manufacture and typically exhibit extreme pixel-to-pixel response nonuniformity as well as many dead pixels. Hence, they require periodic non-uniformity correction using black-bodies at two different temperatures. After this is done, the images look very nice.
A typical HgCdTe FPA size may be up to about 320×240 pixels, but not more than that unless you are willing to spend extravagant sums of money for a product produced using a low yielding process. In fact, unless you are contracting for the US military, large HgCdTe detectors are probably not available at any price. The cost for the commercially available 320×240 detector may be roughly $50-100k. InSb FPAs are also available, and they have most of the benefits of the HgCdTe technology while avoiding most of its problems. However, because they are sensitive to shorter wavelengths, they are limited to temperatures above 0°C. And the cost is still high, of course, but not shockingly so.
The other common detector type used for thermal imaging is the microbolometer. These sensors use materials with a high temperature coefficient of resistance such as amorphous silicon (relatively easy to manufacture) or vanadium(V) oxide (higher TCR), and the FPA is constructed from a grid of tiny thermally isolated resistors exposed to incident thermal radiation. Because they measure temperature directly, they are sensitive over a wide spectral range. These detectors have fewer problems with uniformity, and because a change in resistance is being measured instead of a current, there is no problem with thermally generated carriers. The sensor can thus be operated at room temperature after initial calibration for the resistance of the individual elements. The readout circuitry is also cheaper because it can be row-column multiplexed, which is acceptable because the thermal time constant is such that instantaneous readout would not be possible anyway. However, it is difficult to manufacture the FPA so that the resistors are all equally well thermally isolated from the substrate and one another, and measuring their resistance does of course entail passing current through them, which can change their temperature. For these reasons the image does look more grainy than from a HgCdTe or InSb FPA, the NETD is higher, and the frame rate is lower. But, it is more than sufficient for many thermography applications, and the cost is much lower than the photoconductive detectors. With the rise of silicon-based microbolometers, they have essentially become commodity products.
If you are seriously thinking about thermal imaging for a particular application, the most appropriate advice would probably be to contact a manufacturer of thermal imaging cameras and ask for a demonstration. There are many companies serving this market, but FLIR Systems has an extraordinarily wide range of products and in recent years has been increasingly catering to scientific users, so they would be one of my first contacts personally.
Footnote: to clear up some terminology arising in comments: thermal infrared (roughly 3-20µm or sub-bands within that) is in the mid-infrared spectral region. Within this we have the mid-wave (3-7µm) and long-wave (7-20µm) infrared bands. These definitions are quite approximate and the borders between them depend largely on the availability of detector materials and the specific application. However, "far infrared" refers to wavelengths of roughly 20-100µm, which correspond to lower-than-ambient temperatures: this spectral region has few practical applications and is mainly of scientific interest. There are also the short-wave infrared (1.5-3µm) and near-infrared (700-1500nm) regions, which are sometimes used for non-contact temperature measurements of hot objects, but otherwise are not normally considered thermal.