An alternative for nvidia cards is to use nvidia-smi: the "NVIDIA System Management Interface program".

user@box:~$ nvidia-smi -q -d temperature

GPU 0:

            Product Name            : GeForce 210

            PCI ID                  : a6510de

            Temperature             : 39 C

Or to output just the numeric value in Celsius:

user@box:~$ nvidia-smi --query-gpu=temperature.gpu --format=csv,noheader

39

The already mentioned command for nvidia (on my OpenElec installation):

nvidia-smi

also gave additional information:

+------------------------------------------------------+                       

| NVIDIA-SMI 3.295.71   Driver Version: 295.71         |                       

|-------------------------------+----------------------+----------------------+

| Nb.  Name                     | Bus Id        Disp.  | Volatile ECC SB / DB |

| Fan   Temp   Power Usage /Cap | Memory Usage         | GPU Util. Compute M. |

|===============================+======================+======================|

| 0.  GeForce GT 520            | 0000:01:00.0  N/A    |       N/A        N/A |

|  N/A   52 C  N/A   N/A /  N/A |  17%  169MB / 1023MB |  N/A      Default    |

|-------------------------------+----------------------+----------------------|

| Compute processes:                                               GPU Memory |

|  GPU  PID     Process name                                       Usage      |

|=============================================================================|

|  0.           Not Supported                                                 |

+-----------------------------------------------------------------------------+

If you want to watch the temperature in your terminal for monitoring, you can use watch with the commands that were given in the other answers (e.g. @drgrog's). For instance, to refresh the temperature every 5 seconds:

watch -n 5 nvidia-smi --query-gpu=temperature.gpu --format=csv,noheader

For nvidia there is an nvidia-settings package, which includes a gui to see the temperature. I don't recall if there is a text-mode tool in there.

Some Intel graphics adapters report their temperature through acpi and you can read it through the sensors command from the package of the same name.

I have recently found a cool extension for Gnome 3. So if you are using it - you can install this and see the temperature in the tray:

https://extensions.gnome.org/extension/541/nvidia-gpu-temperature-indicator/

This indicator also includes GPU temp (as well as CPU and HDD temps.)

https://launchpad.net/indicator-sensors

After installing nvclock, just running:

nvidia-settings

On a terminal worked well on GeForce 210 card on top of Ubuntu 14lts.
You get a very nice GUI and can check the celsius temperature at GPU 0 > Thermal Settings.

GPU Temperature with Conky

Conky is a light weight (on resources, not features) system monitor popular in Linux. You can use it to constantly display GPU temperature along with other system elements you like to follow.

Most laptops with nVidia GPUs also include an Intel Integrated GPU (iGPU) for use when on battery power.

My Conky display changes depending on whether Intel or nVidia is selected.

Below are GIFs for nVidia and Intel before and running glxgears to tax the GPU. I'll try to find a more demanding graphics test than glxgears in the future.

Display for Laptop with NVIDIA active

Here's what my Conky looks like when prime-select nvidia is active:

Initially there is low load on nVidia GPU and it's running at 746 MHz and is 55 degrees Celsius. After running glxgears GPU speed spikes to max speed of 1037 MHz and temperature climbs to 58 degrees Celsius.

Display for Laptop with Intel Integrated GPU active

Here's what my Conky looks like when prime-select intel is active:

Initially there is low load on Intel Integrated GPU (iGPU) and temperature (of CPU) is 49 degrees Celsius. After running glxgears CPU temperature climbs to 73 degrees Celsius!

Conky code

Here is the relevant conky code for above:

#------------+

# Temperature|

#------------+

#${color1}All CPUs ${color green}${cpu}% ${goto 131}${color1}Temp: ${color green}${execpi .001 cat /sys/class/thermal/thermal_zone7/temp | cut -c1-2}°C ${alignr}${color1}Up: ${color green}$uptime

# Next line is for kernel >= 4.13.0-36-generic

${color1}All CPUs ${color green}${cpu}% ${goto 131}${color1}Temp: ${color green}${hwmon 1 temp 1}°C ${alignr}${color1}Up: ${color green}$uptime

# Next line is for temperature with Kerenel 4.4

#${color1}All CPUs ${color green}${cpu}% ${goto 131}${color1}Temp: ${color green}${hwmon 0 temp 1}°C ${alignr}${color1}Up: ${color green}$uptime

${color green}$running_processes ${color1}running of ${color green}$processes ${color1}loaded processes.

${color1}Load Average 1-5-15 minutes: ${alignr}${color green}${execpi .001 (awk '{printf "%s/", $1}' /proc/loadavg; grep -c processor /proc/cpuinfo;) | bc -l | cut -c1-4} ${execpi .001 (awk '{printf "%s/", $2}' /proc/loadavg; grep -c processor /proc/cpuinfo;) | bc -l | cut -c1-4} ${execpi .001 (awk '{printf "%s/", $3}' /proc/loadavg; grep -c processor /proc/cpuinfo;) | bc -l | cut -c1-4}

#------------+

# Intel iGPU |

#------------+

${color orange}${hr 1}${if_match "intel" == "${execpi 99999 prime-select query}"}

${color2}${voffset 5}Intel® Skylake GT2 HD 530 iGPU @${alignr}${color green}${execpi .001 (cat /sys/class/drm/card1/gt_cur_freq_mhz)} MHz

${color}${goto 13}Min. Freq:${goto 120}${color green}${execpi .001 (cat /sys/class/drm/card1/gt_min_freq_mhz)} MHz${color}${goto 210}Max. Freq:${alignr}${color green}${execpi .001 (cat /sys/class/drm/card1/gt_max_freq_mhz)} MHz

${color orange}${hr 1}${else}

#------------+

# Nvidia GPU |

#------------+

${color2}${voffset 5}${execpi .001 (nvidia-smi --query-gpu=gpu_name --format=csv,noheader)} ${color1}@ ${color green}${execpi .001 (nvidia-smi --query-gpu=clocks.sm --format=csv,noheader)} ${alignr}${color1}Temp: ${color green}${execpi .001 (nvidia-smi --query-gpu=temperature.gpu --format=csv,noheader)}°C

${color1}${voffset 5}Ver: ${color green}${execpi .001 (nvidia-smi --query-gpu=driver_version --format=csv,noheader)} ${color1} P-State: ${color green}${execpi .001 (nvidia-smi --query-gpu=pstate --format=csv,noheader)} ${alignr}${color1}BIOS: ${color green}${execpi .001 (nvidia-smi --query-gpu=vbios_version --format=csv,noheader)}

${color1}${voffset 5}GPU:${color green}${execpi .001 (nvidia-smi --query-gpu=utilization.gpu --format=csv,noheader)} ${color1}Ram:${color green}${execpi .001 (nvidia-smi --query-gpu=utilization.memory --format=csv,noheader)} ${color1}Pwr:${color green}${execpi .001 (nvidia-smi --query-gpu=power.draw --format=csv,noheader)} ${alignr}${color1}Freq: ${color green}${execpi .001 (nvidia-smi --query-gpu=clocks.mem --format=csv,noheader)}

${color orange}${hr 1}${endif}