No.
There are different pain measures approached in a trial by Joshua Aviram, Tamar Shochat, Dorit Pud in their study of 2015. Pain relating to heat, to cold and to mechanical stress (eg. lifting weights).
It was found that heat and cold pain was better tolerated in the morning while mechanical pain showed no significant difference:
Pain scores varied significantly in six pain parameters during the
day. Specifically, lower pain scores were found in the morning for
cold pain threshold (in seconds and in °C), cold pain intensity, cold
pain tolerance, heat pain threshold and intensity. There were no
significant diurnal differences in the mechanical evoked pain
parameters or in either of the "dynamic" pain paradigms.
By way of explanation, it is suggested that hormone levels play a part:
The results of this study may be partially explained by a potential
analgesic effect of some hormones known to have diurnal variation
(e.g., melatonin and cortisol).