Is Commercial Tenant Holdover different from Residential?

Have Comm/Indust Tenant (small garage-type bldg.) on month-to-month lease, who is refusing to pay rent increase though Lease calls for it. Only is paying the old rent. Tenant has refused our install of electric heat though Lease calls for it. Tenant chose to provide own heat. Now refuses increase claiming no heat when he refused our attempts to provide it to the building. (previous letters to him have addressed this problem). We gave him choice to vacate or provide his own heat. He stayed and continued to pay rent. Now property is up for sale and he refused July rent increase. Want to do a Sept. Holdover, giving him 30-day notice, but what should I do if he continues to pay August rent at old rate. Should I accept it as use and occupancy or not accept the rent because it is not in full? If I accept the old rent amount, will the fact that he has told co-landlord that he is refusing increase based on no heat symbolize that I accept his reason for not paying in full? Thank you.