PA28 pilot reported Electrical System malfunction inflight.

Narrative

Plane was preflighted the night prior; oil levels above 6 QTs. and fuel was topped 24 gallons each tank. Battery was on trickle charger; oil pan was plugged in for heat and a ceramic heater with duct was put to preheat the engine/cowling. Morning of flight; plane was looked over; all exterior lights still functioning and controls were checked. Plane was loaded with two family members. I filed IFR days in advance. Departed from ZZZ airport and picked up IFR airborne with ZZZ1 TRACON leaving 3000. I was intercepting the airway when I received my rerouting of 'Aircraft X cleared to the ZZZ2 airport; direct ZZZ3 then direct destination; climb and maintain 5000;' I read back my clearance. After being handed off to ZZZ TRACON; roughly 15 NM on the 292 bearing of ZZZ3; I started seeing indications of electrical. My temperature gauge in the plane started climbing excessively at one point indicating 200F. The audio panel and GPS equipment started showing 'rainbow' stripes and fading in and out as if it was blacked out. The reading on the ALT AMPS was 0. My electrical turn coordinator was also inoperative at the time during flight; indicated a red flag on the instrument. Communication between ZZZ TRACON and myself was scratchy; I could barely hear and I was unsure if they were able to hear me. ZZZ offered me lower altitude. In my head I was questioning if the cold temperatures affected the battery. I stated I would like to descend to 3000 ft. to better temperature in hopes to stop the problem. ZZZ TRACON asked me if I was declaring an emergency; I stated 'Negative Emergency' and just reassured I was requesting to return to ZZZ.After informing them of my electrical issue; I requested to return to ZZZ knowing the problem was electrical; nothing mechanic or power of engine. ZZZ TRACON offered to land at ZZZ1 to troubleshoot; but I believed returning to ZZZ with multiple diversion airports along the way was reasonable and provided me 'safe haven' to divert in worst case scenario. ZZZ [TRACON] asked if I could take the hand off to ZZZ1 TRACON in which I stated I could; they switched me to ZZZ1. In return to ZZZ; ZZZ1 asked if I could take the last hand off to their other frequency and if I could not they would work that sector; I informed them I could take the hand off. The Controller also asked me to confirm the state of emergency; and I reassured the Controller I was operating on backup battery and standby equipment; and I was 'Negative Emergency.' Over the ridge line just north of ZZZ4 field; Controller came across 'Aircraft X radar contact lost; state position and altitude.' I returned with the requested information. I cancelled my IFR on the ground via the 1-800 number to ZZZ1 TRACON. After returning to ZZZ; we checked the voltage on the battery and it read 8.5V. After discussing with fellow pilots and the primary owner of the plane; we contacted a maintenance shop on the field to inspect the alternator and voltage regulator to handle any replacements and/or fixes that are in need. The plane landed safely without injury or damage. Controllers inquired if I was 'emergency aircraft' and I responded every time that I was 'negative emergency.'