I have a Rinnai R85 water heater and my temperature controller doesn't have any power.

I could not find r85 model on rinnai website. There is a troubleshooting guide on rinnai website. 100000652-Troubleshooting TWH Diagnostic Codes.pdf (rinnai.us) It may help to find a solution.

possible bad power transformer or unit is overheating

https://www.rinnai.us/?gclid=CjwKEAiAjcDBBRCJxouz9fWHynwSJADaJg9BCOsG1J5MZeqcKsVrstipRg-yKszKLTUR6DbZAV0DdxoC1dHw_wcB

[PDF]Operation / Installation Manual - Rinnai

https://www.rinnai.us/.../V_Series_Indoor_25xx_U...

Rinnai America Corp.temperature (shown on the digital remote control) the gas burner will ... Without the connection of a remote controller(s), the Rinnai Water Heater is preset to.

PDF]Tankless Water Heater Service Manual - Rinnai

https://www.rinnai.us/.../100000098_Rev_B.pdf

Rinnai America Corp.Indicates condensing water heater models. ... Rinnai Water Heater Service Manual. 2 ..... Digital manometer or U tube type manometer with 14 inch water column (W.C.) scale, a hose and two .... will flash on the display of the remote controller.

I went to the Rinnai website and this is what I found for error code 61.
Error Code 61 Problem: Fan failure
Solution: Measure the resistance on the fan motor, check the damaged or loose wiring and connections. Make sure that the fan spins freely.
Sounds like either your fan is broken or something is keeping it from spinning freely.
Hope this helps.
Gary

Probably frozen. Let it thaw out and see if it works. You may want to think about wrapping the pipes with heat tape because of those low tempertures they could break especially if the unit is outside.

Good luck,

Marty

The manual says:
http://www.coinwash.com/temp/rinnai.pdf

"For the name of the Authorized Distributor or Installer nearest you, please contact your local HVAC dealer or gas service technician, visit the Rinnai website (www.rinnai.us), call Rinnai at1-800-621-9419 or write to Rinnai, 103 International Drive, Peachtree City, Georgia 30269"

Manual says that the remote is for setting temperature.
When you turn on hot water spigot, tankless water heater will heat the water to the set point temperature.
If water heater is not set up to use remote, then tankless unit will heat to 140 degrees F.
"With the MCC-45-4US remote control installed the water temperature is adjustable from 96
to 180°F. The water temperature cannot be set to a temperature other than 140°F
without the use of the MCC-45-4US remote control unit. If you require a temperature
other than 140°F you must install the MCC-45-4US remote control unit."

"Error messages are displayed on the remote control units, simplifying service calls."

Page 9 of manual shows hot to set temperature using remote.
Water taps must be shut off to set temperature.
Circulating pump must be turned off.
"Simply press the H or C button until desired temperature is displayed"
"green in-use indicator will display"

If your unit is not working, the manual says to contact local plumber.
Fixya has specialists who will talk to you by phone about your problem for a fee.

I just fixed a leaky R85. Fortunately it's the bypass valve, not the heat exchanger. Did your heater freeze up in this snow storm? Unplug the power, open the cover and see where it leaks. If water comes from the top, means crack on the heat exchanger, then it would be too costly to replace. If you can see the water gushing out of a valve, on the bottom of the heater, then it's an easy fix. The valve is fixable, you don't have to replace it. But still need to find out what causes the flame fail (error 12). I suspect the igniter got wet, dry it with a towel after you take out the valve. Removing the fan first will give you more room to work inside.

Power outage will reset Rinnai unit to that temperature. Read manual for more info.

Sounds like there is something loose in the line.Like cut off valve,check valve.