There are two ways to answer your question: the first would be by verifying historical forecast data (calculating the difference to observed temperatures) and looking into a temperature dependency of these errors. This would certainly be doable - but in this context on Stackexchange not.
So I suppose you refer to a general, more physically interpretable explanation what the difference in forecasting higher or lower temperatures is.
Even though it makes a difference for physical processes like radiation and evaporation if temperatures are high or low, the characteristics stay the same - more explicitly said:
Temperature differences matter more than absolute temperatures!
The net radiation (budget) is proportional to the difference of soil and atmospheric temperature (each to the fourth power).
Deeper layers of soil keep the surface warm by transporting heat (also proportional to the temperature difference).
and so on...
But there is a significant difference in the active physical processes:
At daytime (Tmax), the near surface air is (mostly) coupled to the temperature of higher layers of air by turbulence. On a sunny summerday, the surface air can not get significantly warmer than the air above because if it gets warmer, the air rises and cooler air from above cools the surface layer. In this way, the surface air temperature is 'tied down' so that it can not reach extrordinary temperatures without also heating up a say 1500 m boundary layer of air.
If the surface air is cooler than the air above it gets decoupled from the temperatures above - turbulence is reduced, and theoretically the temperatures could drop a looong way down, until the incoming (longwave) radiation from the atmosphere (say hi to greenhouse gases) stops this temperature drop. The equilibrium temperature depends mostly on the amount of water vapor above our heads -> warmer in the tropics, cooler nights in polar regions. But the equilibrium is practically never reached. In most cases it is a dynamic thing with ground heat flux and sporadic wind gusts - which are of very local effect.
Comparing these two cases one can see that the Tmax is more homogenously distributed in space because it mostly depends on the airmass. Minimum temperatures can be very different even for close locations because it really depends on your surrounding: trees, buildings, ridges. You can see the lowest Tmin at high altitude locations which are not exposed to wind gusts (sinkholes) which are covered by snow (isolated from soil heat).
So by analyzing a forecast error dataset, you would most likely see that Tmax are more accurately forecast.