Of course, clowns and unicycles are two entirely unrelated phenomena, and should remain so.
However, ‘proper’ clowns don’t wear ‘clamp on’ or ‘stick on’ plastic or foam noses. They mould a nose on with a ‘clay’ or ‘putty’ like substance.
It is possible to buy a special ‘clay’ from a theatrical supplier. However, a good substitute is lard, mixed with red cayenne pepper for the colourant. This is the traditional solution used by real clowns, but it can cause problems for the amateur who does not have the advantage of circus inbreeding. A clown from one of the traditional circus families is likely to have up to 47% fewer capillaries in the proboscal epidermis.
So for an amateur, the combination of covering the pores on the nose, and applying cayenne pepper, can result in the nose over heating. Not only is this uncomfortable, but the heat generated can be sufficient to melt the lard, causing it to distort and slip own towards the chin. This is the historical origin of the rather strange shape of Mr. Punch’s face in Punch & Judy shows.
Traditionally, clowns were able to cope with this, partly by the reduced capillary density mentioned above, and partly by only performing in big cold draughty tents, or in street parades, where it normally rains. This may not be sufficient for an amateur.
However, if you are unicycling, you can add the wind chill factor. This is proportional to the square of your airspeed, so if you opt to use the lard and cayenne pepper moulded nose, ensure that you ride at a brisk speed.
Of course, you might say that riding fast can be counterproductive because it generates additional heat from metabolism, and you’d be right. So ride a big wheel like a Coker, as this has less rolling resistance, meaning you get the maximum speed (and cooling effect) for minimum effort (and metabolism).
You will note that those few clowns who actually use unicycles tend to ride giraffes. The additional height helps with cooling, because temperature falls with altitude.
The maths gets complicated (Klaas Bil may be able to help here) but the consensus seems to be that unicycling and clowning should be kept separate at all times. Imagine the chaos if your lard nose melts and part of it drops onto the tyre. An emergency stop could result in a lengthy skid, possibly causing injury to the rider and members of the public.