I can picture any number of mechanisms by which a shift could happen (eg. more cars driving past the thermometer at the time the measurements are taken), so has such a shift been found?
Firstly you need to define what you mean by average daily temperature. What algorithm are you going to use to compute it (from several time spaced measurements), why and what do you think the result represents.
Obviously if you use a measurement which is going to be affected by very local anthropogenic activity (e.g. cars) you can expect timing of activities to affect individual measurements. a measuring station which is going to be thus affected is not really going to be useful for anything wider or general though.
When siting weather stations we try to find locations which are not subject to such local disturbances. Ideally well away from any heat producing apparatus (e.g. fixed a/c units), heated buildings, variable traffic and so on. Locations in open non urban areas are preferable for understanding changes in the weather and climate. Past locations thus chosen however have often been compromised by the expansion of nearby housing or industry as populations and cities have expanded. This is why you sometimes see references to Urban Heat Islands (UHI) in discussions of climate measurement.