In an early report on the matter [Hoag] measured at the Flagstaff 1.5-m telescope of the US Naval Observatory, housed in a dome with a diameter of 20 m, the correlation between seeing and the temperature difference between the inside and outside air, finding a mean dependency of 0.28 arcsec/K.
[Murdin] measured the increase of image size caused by dissipating large powers inside the dome volume. The heat was generated by electrical fan-heaters. In the Isaac Newton Telescope dome (located at that time at Heastmonceux, GB) which has a diameter of 18 m, the increase of seeing FWHM was found to follow approximately a linear relationship with slope 0.052 arcsec/kW. At the Yapp 90-cm telescope dome (diameter 9 m) the slope was 0.11 arcsec/kW. In both cases the warm air was blown inside the dome but not directly in the telescope beam. When the air blown by an electric fan heater rated 3 kW was directed into the telescope beam the degradation climbed to a few arcseconds per kW. Although these experiments were not representative of actual dome seeing conditions, since the average heat dissipation of telescopes and instruments seldom exceeds a few kilowatts and of course warm air is never blown into the optical beam, the results prompted telescope designers and operators to require the active cooling of the electro-mechanical and electronic systems of most following telescope. In other tests, the experimenters also dissipated 90 kW just outside and upwind of the dome slit, but could not detect a sensible degradation. Nevertheless it is also customary to require that the heat dissipation from all telescope circuits is done away and downwind from the dome.
[Woolf 79] formulated a theory of dome seeing based on the assumption that turbulent "bubbles" of warm air fill the dome volume. We note that this assumption is in contrast with a correct description of free convection in a large volume (see for instance [Townsend]) whereby the regions away from the surfaces may experience large velocity means and fluctuations but negligible temperature fluctuations, which are confined to the wall regions. Later, however, Woolf himself relativized the significance of his early interpretation in [Woolf 82] and [Woolf 82a] (which is a very comprehensive review of the seeing subject) and expressed the hypothesis that mirror seeing is more responsible for poor seeing than any other factor in telescope design.
[Gillingham 82] measured at the Anglo-Australian Telescope a correlation of
0.28 arcsec/
C between seeing and the temperature difference
between the inside and outside air.
Some of his observations on the effects of blowers on dome
seeing have been cited in section 
above.
[Forbes 82] performed some measurements of temperature
fluctuations inside the enclosure of the Multi-Mirror Telescope (see
section and fig. above).
He noted a loose relationship between local microthermal activity
inside the dome and image blur.
[Woolf 88] did some order-of-magnitude estimates of possible dome
seeing effects. He analyzed experimental measurements from the AAT,
the CFHT (see section ) and the University of
Hawaii 88-inch telescope, which indicated the likelihood that seeing
was caused mostly by a mirror-air temperature difference.
The CFHT observatory (see section ) brought a
particular attention to the analysis and improvement of seeing quality.
[Racine 92] analyzed 562 image frames from the HRCam instrument
(for high resolution imaging) taken during 25 nights
for correlations with temperature differences.
He found that the main contribution to local seeing was due to
occurrences of positive surface-air temperature differences at the
optical surface of the primary mirror, while
a less significant dependency was found with the temperature difference
between the dome inside and outside air.