Spreading disease between trees is a real concern once you get too late in the spring. Warmer temps mean active bugs/beetles and freshly cut trees can be an open invitation for them.
There is an old saying that I am going to butcher that goes something like this, "May or June...do not prune."
The red oak family of trees is particularly susceptible to oak wilt and it can be spread during these warmers months. I personally would not do much TSI work after about the 1st of April. Google "oak wilt" and you will get more/better info than what I am giving here.